Lecture_15.ipynb

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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from IPython.display import Image\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lecture 15:\n",
    "\n",
    "- Learn some basic statisics - samples versus populations and empirical versus theorectical distributions.\n",
    "\n",
    "- Learn to calculate _central tendencies_, _spreads_. \n",
    "\n",
    "- Learn about _significant figures_ and more about formatting output. \n",
    "\n",
    "- Learn some useful functions in **NumPy** and **SciPy** for simulating distributions and calculating statistics."
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Basic statistical concepts\n",
    "\n",
    "Much of this lecture has been cribbed from the open source paper by Olea (2008) available in its entirety here:  https://pubs.usgs.gov/of/2008/1017/ofr2008-1017_rev.pdf which in turn was cribbed from Davis, J. (2002: Statistical and Data Analysis in Geology, 3rd Ed, Wiley, Hoboken).  \n",
    "\n",
    "While this is not a class in statistics, many Earth Scientists write programs to calculate statistics, evaluate significance, and estimate _averages_ and their uncertainties.\n",
    "\n",
    "So, what is (are?) statistics?  Statistics is the way we analyze, interpret and model data. To do it properly we need to understand a few concepts: \n",
    "\n",
    "1) **accuracy** versus **precision**:  accuracy is how close your data are to the \"truth\" while precision is the reproducibility of your data.  \n",
    "\n",
    "2) **population** versus **sample**: the _population_ is the set of all possible outcomes of a given measurement (if you had an infinite number of data points), while the _sample_ is what you have - a finite number of data points.  \n",
    "\n",
    "3) **probability**: Probability is the measure of how likely it is for a particular event to occur.  If something is impossible, it has a probability ($P$) of 0.  If it is a certainty, it has a probability $P$ of 1.  \n",
    "\n",
    "4) **Theoretical** versus **empirical** distributions: Empirical distributions are measured data. Theoretical distributions are analytical  probabililty functions (mathematical equations) that can be described with an equation.  These can be applied to  data, allowing interpretations about the likelihood of observing a given measurement, whether  sets of data are \"different\" from theoretical or other empirical data sets and other powerful statistical tests.  \n",
    "\n",
    "Now we will go through each of these concepts in a bit more detail. \n",
    "\n",
    "## Accuracy versus precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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   "outputs": [
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "image/png": {
       "width": 700
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename='Figures/accuracy_precision.png',width=700)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Figure from https://pubs.usgs.gov/of/2008/1017/ofr2008-1017_rev.pdf ](https://pubs.usgs.gov/of/2008/1017/ofr2008-1017_rev.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Populations versus samples\n",
    "\n",
    "The population is what you would have if you had all possible outcomes - but you never do. We can describe the distribution of a population by using  equations which will predict, say, the fraction of measurements (the _density_) expected to fall within a given range ($x$ between 0 and 1), assuming a particular theoretical distribution.  This curve is called the _probability density function_.  \n",
    "\n",
    "There are equations describing many different types of distributions and evaluating the equations gives us a theoretical distribution. In this lecture, we will look at a few common distributions (_binomial, uniform, normal,_ and  _log-normal_).   \n",
    "\n",
    "Samples are finite collections of observations which may belong to a given distribution. In this lecture, it will be handy to   simulate 'measurements' by drawing 'observations' from a theoretical distribution, instead of making actual measurements.  This is the _Monte Carlo_ approach (after the gambling town).\n",
    "\n",
    "\n",
    "Examples of theoretical versus empirical distributions:\n",
    "\n",
    "### Binomial distribution:\n",
    "\n",
    "#### Theoretical\n",
    "\n",
    "Perhaps the most straight forward distribution is the _binomial_ distribution which describes the probability of a particular outcome when there are only two possibilities (yes or no, heads or tails, 1 or 0).   For example, in a coin toss experiment (heads or tails), if we flip the coin  $n$ times, what is the probability of getting $x$ 'heads'?  We assume that the probability $p$ of a head for any given coin toss is 50%; put another way $p$ = 0.5.  \n",
    "\n",
    "The binomial distribution can be described by an equation: \n",
    "\n",
    "$$P=f(x,p,n)= \\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}, x=0,1,2,...,n.$$\n",
    "\n",
    "We can look at this kind of distribution by evaluating the probability for getting $x$ 'heads' out of $n$ attempts using our old friend from Lecture 11, the **lambda** function. We'll code the equation as a **lambda** function, and calculate the probability $P$ of a particular outcome (e.g., $x$ heads in $n$ attempts).  We can collect all the answers in a list and  plot the probability ($P$) versus the number of heads ($x$) out of $n$ attempts.  \n",
    "\n",
    "Here is a **lambda** function called **Binomial**, which returns the probability of a given number of heads ($x$) out of $n$ attempts.  Note that for a coin toss, $p$ is 0.5, but other yes/no questions can be investigated as well (e.g., chance of winning the lottery given purchase of $n$ tickets).  Oh and we finally have a use for the **np.factorial( )** function we ran accross in Lecture 11.  Or you could our own **reduce** funtion. :)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Binomial=lambda x,n,p :(np.math.factorial(n)/(np.math.factorial(x)*np.math.factorial(n-x)))\\\n",
    "                   *(p**(x))*(1.-p)**(n-x)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use **Binomial** to look at the predicted likelihood of getting $x$ heads out of $n=12$ attempts (coin tosses) with a $p$ (probability) of 0.5. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    " # calculate the probability  of x heads in n attempts with a probability of 0.5\n",
    "n,p=12,0.5 # number of attempts in each trial, probability of getting a head\n",
    "xs=range(n+1) # range of test values from 0,N\n",
    "Probability=[] # probability of getting x heads out of n attempts\n",
    "for x in xs: # step trough the test values\n",
    "    Probability.append(Binomial(x,n,p))# collect the theoretical probability of getting x heads\n",
    "plt.bar(xs,Probability,width=.5,color='cyan') # plot as bar plot\n",
    "plt.plot(xs,Probability,'r-',linewidth=2) # plot as solid line\n",
    "plt.xlabel('Number of heads out of $n$ attempts') # add labels\n",
    "plt.ylabel('Probability') \n",
    "# place a note in upper left in axes coordinates with a fontsize of 14.\n",
    "plt.text(1,.2, 'n = %i'%(n),  fontsize=14)\n",
    "plt.title('Binomial Distribution');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Red line is the theoretical probability distribution function.  Cyan bars are the same, but plotted as a bar graph._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I plotted the outcome as both a bar plot and a solid red line, to demonstrate two different ways of visualizing the results. Note that the red line is the _probability density function_.  \n",
    "\n",
    "What you learn from this is that the most probable outcome is 6 out of 12 heads (with a $P$ of ~23%),   but other outcomes can very well occur.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Empirical\n",
    "\n",
    "One great feature about computers is that we can simulate a data sample to compare to our theoretical predictions. \n",
    "We can use the module **numpy.random** to generate examples of  simulated data sets in a process called _Monte Carlo simulation_.  We encountered **numpy.random( )** in the Lecture 14 when we used the **random.randint( )** function.  In this lecture we will discover a few more, starting with **random.binomial( )** which generates samples from a _binomial_ distribution. \n",
    "\n",
    "To use all the functions in **random** we must first import it.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on built-in function binomial:\n",
      "\n",
      "binomial(...) method of mtrand.RandomState instance\n",
      "    binomial(n, p, size=None)\n",
      "    \n",
      "    Draw samples from a binomial distribution.\n",
      "    \n",
      "    Samples are drawn from a binomial distribution with specified\n",
      "    parameters, n trials and p probability of success where\n",
      "    n an integer >= 0 and p is in the interval [0,1]. (n may be\n",
      "    input as a float, but it is truncated to an integer in use)\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    n : int or array_like of ints\n",
      "        Parameter of the distribution, >= 0. Floats are also accepted,\n",
      "        but they will be truncated to integers.\n",
      "    p : float or array_like of floats\n",
      "        Parameter of the distribution, >= 0 and <=1.\n",
      "    size : int or tuple of ints, optional\n",
      "        Output shape.  If the given shape is, e.g., ``(m, n, k)``, then\n",
      "        ``m * n * k`` samples are drawn.  If size is ``None`` (default),\n",
      "        a single value is returned if ``n`` and ``p`` are both scalars.\n",
      "        Otherwise, ``np.broadcast(n, p).size`` samples are drawn.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    out : ndarray or scalar\n",
      "        Drawn samples from the parameterized binomial distribution, where\n",
      "        each sample is equal to the number of successes over the n trials.\n",
      "    \n",
      "    See Also\n",
      "    --------\n",
      "    scipy.stats.binom : probability density function, distribution or\n",
      "        cumulative density function, etc.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    The probability density for the binomial distribution is\n",
      "    \n",
      "    .. math:: P(N) = \\binom{n}{N}p^N(1-p)^{n-N},\n",
      "    \n",
      "    where :math:`n` is the number of trials, :math:`p` is the probability\n",
      "    of success, and :math:`N` is the number of successes.\n",
      "    \n",
      "    When estimating the standard error of a proportion in a population by\n",
      "    using a random sample, the normal distribution works well unless the\n",
      "    product p*n <=5, where p = population proportion estimate, and n =\n",
      "    number of samples, in which case the binomial distribution is used\n",
      "    instead. For example, a sample of 15 people shows 4 who are left\n",
      "    handed, and 11 who are right handed. Then p = 4/15 = 27%. 0.27*15 = 4,\n",
      "    so the binomial distribution should be used in this case.\n",
      "    \n",
      "    References\n",
      "    ----------\n",
      "    .. [1] Dalgaard, Peter, \"Introductory Statistics with R\",\n",
      "           Springer-Verlag, 2002.\n",
      "    .. [2] Glantz, Stanton A. \"Primer of Biostatistics.\", McGraw-Hill,\n",
      "           Fifth Edition, 2002.\n",
      "    .. [3] Lentner, Marvin, \"Elementary Applied Statistics\", Bogden\n",
      "           and Quigley, 1972.\n",
      "    .. [4] Weisstein, Eric W. \"Binomial Distribution.\" From MathWorld--A\n",
      "           Wolfram Web Resource.\n",
      "           http://mathworld.wolfram.com/BinomialDistribution.html\n",
      "    .. [5] Wikipedia, \"Binomial distribution\",\n",
      "           http://en.wikipedia.org/wiki/Binomial_distribution\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    Draw samples from the distribution:\n",
      "    \n",
      "    >>> n, p = 10, .5  # number of trials, probability of each trial\n",
      "    >>> s = np.random.binomial(n, p, 1000)\n",
      "    # result of flipping a coin 10 times, tested 1000 times.\n",
      "    \n",
      "    A real world example. A company drills 9 wild-cat oil exploration\n",
      "    wells, each with an estimated probability of success of 0.1. All nine\n",
      "    wells fail. What is the probability of that happening?\n",
      "    \n",
      "    Let's do 20,000 trials of the model, and count the number that\n",
      "    generate zero positive results.\n",
      "    \n",
      "    >>> sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.\n",
      "    # answer = 0.38885, or 38%.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from numpy import random\n",
    "help(random.binomial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate some  data, you could either patiently do the experiment with a coin toss, or we can just use the **random.binomial** function to simulate 'realistic' data.  \n",
    "\n",
    "**random.binomial( )** requires 2 parameters, $n$ and $p$, with an optional keyword argument **size** (if **size** is not specified, it returns a single trial).   Each call to **random.binomial( )** returns the number of heads flipped in a single trial of $n$ coin tosses, given the probablity $p=0.5$. \n",
    "\n",
    "Let's try it with $n=12$ and $p=0.5$.  This little code block returns the number of heads out of $n$ attempts. You will get a different answer every time you run it.  It also gives the probabilty of getting that result from our lambda function **Binomial( )**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 heads, with a likelihood of:  0.193359375\n"
     ]
    }
   ],
   "source": [
    "n,p=12,0.5 # same as before\n",
    "x=random.binomial(n,p) # size = 1 by default\n",
    "print (x, 'heads, with a likelihood of: ',Binomial(x,n,p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " As the number of times you repeat this 'experiment' approaches infinity, the distribution of outcomes will approach the theoretical distribution (i.e., you will get an average of 9 heads out of 12 attempts 5% of the time).   \n",
    "\n",
    "So let's compare the results simulated via Monte Carlo for some number of experiments ($Nmc$) with the theoretical distribution.  To do this,  we pretend that each student in the class ($Nmc=20$) flips a coin $n=12$ times and reports the number of heads.  We can collect the number of heads flipped by each student in a list called **Simulated**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n,p=12,0.5\n",
    "Nmc=20 # number of simulated experiments each with n  attempts\n",
    "Simulated=random.binomial(n,p,size=Nmc)\n",
    "plt.bar(xs,Probability,color='cyan', label='Theoretical') # theoretical curve as bar graph\n",
    "plt.hist(Simulated,density=True,color='orange',histtype='step',linewidth=3, label='Simulated') # note the normed key word - \n",
    "    #  this normalizes the total to be unity\n",
    "plt.xlabel('Number of heads out of $n$ attempts')\n",
    "plt.ylabel('Fraction of simulated experiments')\n",
    "plt.text(1,.3, 'n = %i'%(n),  fontsize=14)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Orange line is the Monte Carlo results.  Blue line is the theoretical probability distribution function from before._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that every time you repeat this, the Monte Carlo results are a little different.  And if you change $Nmc$ to be, say 10, you get more and more \"weird\" results.  But if you set $Nmc$ to 5000 - your results would look consistently  closer to the theoretical predictions. \n",
    "\n",
    "It is worth pointing out here that it is possible to make sure that every time you repeat a \"random draw\" that you get the SAME answer (for reproducibility of your code, for example if you share it with others).  To do this you can use the **random.random(seed)** option where $seed$ is set in your program.  Here is  examples with and without the seed: \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "random numbers generated with seed\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "[ 8  6  7  7  8  5  7  8  8  6  6  5  4  8  4 10  3  6  5  8]\n",
      "random numbers generated without seed\n",
      "[6 6 5 8 6 4 5 3 6 6 8 9 7 8 9 8 8 7 4 5]\n",
      "[5 4 6 8 5 5 7 4 6 8 5 5 5 5 5 9 3 7 5 7]\n",
      "[6 7 5 7 5 5 8 8 6 7 5 5 6 6 8 7 9 5 6 5]\n",
      "[5 5 5 6 6 7 4 5 6 6 2 7 7 9 6 6 7 6 5 3]\n",
      "[ 4  7  5  7  7  4  9  8  5  5  4  7  3  5  3 10  4  4  5  6]\n",
      "[5 9 5 6 5 4 9 7 8 5 3 6 3 3 7 6 7 9 5 5]\n",
      "[8 7 8 6 7 4 6 6 5 2 4 4 6 8 7 7 5 9 3 5]\n",
      "[6 6 4 7 6 3 6 6 3 8 6 6 4 4 8 5 6 7 4 6]\n",
      "[ 9  8  6  6 10  4  5  9 10  2  3  4  8  5  7  4  8  4  6  7]\n",
      "[6 6 5 7 7 6 9 6 7 6 6 9 9 6 8 7 5 6 6 4]\n"
     ]
    }
   ],
   "source": [
    "seed=2019\n",
    "print ('random numbers generated with seed')\n",
    "for i in range(10):\n",
    "    random.seed(seed)\n",
    "    print (random.binomial(n,p,size=Nmc))\n",
    "print ('random numbers generated without seed')\n",
    "for i in range(10):\n",
    "    print (random.binomial(n,p,size=Nmc))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of this lecture, we want different random numbers every time, so we will work without the seed.  Also, something about the 'density' (formerly 'normed') keyword in **plt.hist( )**.  According to the **NumPy** documention for  **density**: If it is set to 'True', the result is the value of the probability density function at the bin level, normalized such that the integral over the entire range is 1. But note: the sum of the histogram values will not  equal  1 unless bins of unity width are used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other distributions that we could play with. In the rest of the lecture, we will look at a few of the more common ones in Earth Science:   uniform,  normal and  log normal distributions.   We'll approach each in the same way as for the binomial distributions starting with the theoretical distribution followed by a Monte Carlo simulation of empirical results.  \n",
    "\n",
    "### Uniform distribution\n",
    "\n",
    "#### Theoretical\n",
    "\n",
    "A uniform distribution is pretty much what it sounds like.  All outcomes within the bounds of $a,b$ are equally likely. Outside those bounds, the probability is zero.   For example, when playing dice, what is the likelihood of getting a particular number of dots (1 in 6).\n",
    "\n",
    "The analytical form for a uniform distribution is:\n",
    "\n",
    "$$P=f(x,a,b)= \\frac{1}{b-a},  x=a \\rightarrow b$$\n",
    "\n",
    "where $a$ and $b$ are bounds ($a \\le x<b$). $P$ is the probability of getting a value of $x$.  It is zero if $x$ is not between $a$ and $b$, and  between $a$ and $b$ the probability is a constant. In fact the probability is  $1/n$ where $n$ is  $b-a$, the number of possible outcomes.\n",
    "\n",
    "Say we have a die with 1 to 6 dots on each face.  The probability of getting one dot is 1 in 6, but getting seven dots is zero.  \n",
    "\n",
    "We code up the **lambda** function as before:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Uniform=lambda a,b : (1./(b-a)) # function for calculating P from a uniform distribution.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And calculate the probability density function as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate the probability of returning a value x with a uniform distribution between a,b\n",
    "xs=range(11) # range of possible number of dots from 1 to 10. \n",
    "a,b=1,7 # bounds for the uniform distribution\n",
    "Probability=[] # container for the theoretical results. \n",
    "for x in xs: # step through test values\n",
    "    if x not in range(a,b): # if x<a or x>b,  there is zero probability of rolling this number\n",
    "        Probability.append(0) # save the probability\n",
    "    else: # otherwise\n",
    "        Probability.append(Uniform(a,b)) # get the probability from our little function\n",
    "plt.bar(xs,Probability,color='cyan') # plot as a bar plot\n",
    "plt.title('Uniform')\n",
    "plt.xlabel('Number of dots')\n",
    "plt.ylabel('Probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Empirical\n",
    "\n",
    "And now we can look at the Monte Carlo simulation of an empirical distribution using **random.uniform( )**. \n",
    "\n",
    "So here it is.    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,b=1,7 # keep the same bounds\n",
    "Nmc=20 # number of \"students\" rolling the dice\n",
    "Simulated=random.uniform(a,b,Nmc).astype('int') # get Nmc test values in one go.  :)\n",
    "# the .astype(int) makes this an array of integers, as only integers are possible outcomes\n",
    "plt.bar(xs,Probability, color='cyan',label='Theoretical')\n",
    "# plot results as histogram normed to sum to unity and use histtype of 'step' to make it see-through\n",
    "plt.hist(Simulated,density=True,histtype='step',color='orange',linewidth=3.,label='Simulated') \n",
    "plt.xlabel('Number of dots')\n",
    "plt.ylabel('Fraction')\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two more closely related distributions which we need to discuss:  the normal and the log-normal distributions.  We'll do these with the same approach as before, looking first at the theoretical probability function and then as a Monte Carlo simulation.  \n",
    "\n",
    "### Normal distributions\n",
    "\n",
    "The so-called \"normal\" distribution (also known as a Gaussian distribution after the guy who thought it up) describes data, for example,  measurement data, that have uncertainties associated with them - they are more or less precise.  There is some 'true' answer but all the measurements have some slop. Imagine measuring the width of a sedimentary bed, or the length of a fossil thigh bone or the distance between two points.  The measurement data will have some _average_ (a.k.a. _central tendency_) and some degree of _spread_.  For normal distributions,  the _average_ is the arithmetic _mean_ $\\mu$ and the spread is the _standard deviation_, $\\sigma$.  \n",
    "\n",
    "#### Theoretical: \n",
    "\n",
    "The analytical form for a normal distribution is:\n",
    "\n",
    "$$P=f(x,\\mu, \\sigma)= \\frac{1}{\\sigma\\sqrt{2\\pi}} e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}},-\\infty < x < \\infty$$\n",
    "\n",
    "\n",
    "We can put this equation into a lambda function called **Normal** and work on it as before with one small modification.  We can write the Normal _lambda_ function such that it returns an array if $x$ is passed as an array.  This is a trick called 'vectorization' and is numerically more efficient than calling the function many times and appending to a list of results, for example.  Use this trick any time you can!\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "Normal=lambda x,mu,sigma : (1./(sigma*np.sqrt(2.**np.pi)))*np.e**(-(x-mu)**2/(2.*sigma**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "And, we calculate the probability of observing a measurement $x$ from a normal distribution with $\\mu$ and $\\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu,sigma,incr=10,1,.2 # set the mean,  standard deviation and bin width\n",
    "xs=np.arange(5,15,incr) # make an array of test values\n",
    "Probability=Normal(xs,mu,sigma) # get probabilities \n",
    "plt.bar(xs,Probability,width=incr,color='cyan', edgecolor='k') # make the bar chart\n",
    "plt.plot(xs,Probability,'r-',linewidth=2) # plot as a continuous probability distribution\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability')\n",
    "plt.text(5,.3,'$\\mu$ = '+str(mu)) # stick on some notes\n",
    "plt.text(5,.27,'$\\sigma$ ='+str(sigma))\n",
    "plt.title('Normal');\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That should look a lot like the so-called 'bell curve' - the curve used for grading for example - because that is exactly what it is.  \n",
    "\n",
    "#### Empirical\n",
    "\n",
    "So let's compare the bell curve with some simulated data.  For this, we can use  **random.normal( )**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu,sigma=10,1 # set the mean,  standard deviation\n",
    "Nmc=20 # number of monte carlo simultions\n",
    "Simulated=random.normal(mu,sigma,Nmc) # get Nmc  simulated data points from distribution\n",
    "plt.bar(xs,Probability,width=incr, edgecolor='k',label='Theoretical',color='cyan') # make the bar chart\n",
    "plt.hist(Simulated,density=True,histtype='step',color='orange',linewidth=3.,label='Simulated') # plot them\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We talked about the mean and standard deviation of a theoretical distribution.  Now we  need to learn how to calculate them for our simulated sample (in case you don't know already!).  Note that for the population (as defined above), the average is $\\mu$ but for our _sample_, it is $\\bar x$:\n",
    "\n",
    "$$ \\bar{x} = \\frac{\\sum x_i}{N},$$\n",
    "\n",
    "where $\\sum_{i=1}^N$ means the sum of all individual values of $x$ from the first to the last.\n",
    "\n",
    "Similarly, the standard deviation of the population is $\\sigma$, while for our sample, it is $s$:  \n",
    "\n",
    "$$s = \\sqrt {\\frac {1}{N}\\sum_{i=1}^{N}(x_i-\\bar x)^2 }$$\n",
    "\n",
    "   Note that the _variance_ of the data is $s^2$ (and for the population it is $\\sigma^2$).  \n",
    "\n",
    "With **NumPy**, we can calculate the mean and standard deviation with the methods **.mean( )** and **.std( )** like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of the simulated distribution =  10.086868749412135\n",
      "standard deviation of simulated distribution = 0.8782405911779055\n"
     ]
    }
   ],
   "source": [
    "print ('Mean of the simulated distribution = ',Simulated.mean()) \n",
    "print ('standard deviation of simulated distribution =',Simulated.std()) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to remember about formating and significant figures from a few lectures ago.  For our purposes, only the first few of these trailing decimals are significant, so we should format our print string accordingly.  These are floating point variables and say we want a total of up to, say, 6 characters with two after the decimal point.  We would write this with a string formatting statement with the form '%XXX.XXf'   %(variable).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of the simulated distribution =  10.09\n",
      "standard deviation of simulated distribution =   0.88\n"
     ]
    }
   ],
   "source": [
    "print ('Mean of the simulated distribution = %6.2f'%(Simulated.mean() ))\n",
    "print ('standard deviation of simulated distribution =','%6.2f'%(Simulated.std() ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the mean and $s$ on our histogram:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(xs,Probability,width=incr,color='cyan',label='Theoretical') # make the bar chart\n",
    "#stderr=Simulated.std()/np.sqrt(len(Simulated))\n",
    "plt.hist(Simulated,density=True,histtype='step',color='orange',linewidth=3.,label='Simulated') # plot them\n",
    "plt.plot([Simulated.mean(),Simulated.mean()],[0,.45],'k-',linewidth=2,label='Mean')\n",
    "plt.plot([Simulated.mean()-Simulated.std(),Simulated.mean()-Simulated.std()],[0,.45],\n",
    "         'g--',linewidth=2,label='Standard deviation')\n",
    "plt.plot([Simulated.mean()+Simulated.std(),Simulated.mean()+Simulated.std()],[0,.45],\n",
    "         'g--',linewidth=2,label='_nolegend_') # notice how to suppress a legend entry!\n",
    "plt.ylim(0,.5)\n",
    "plt.legend(loc=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice two things: \n",
    "\n",
    "1) The standard deviation includes ~67% of the data (not 95% - that would be 1.97$\\sigma$, or 2-sigma, informally).  The $\\pm \\sigma$ bounds are the dashed lines in the above plot.  \n",
    "\n",
    "2) The mean of our sample is generally not the same as the mean of the distribution ($\\bar x \\ne \\mu$).  In fact, the 95% confidence bounds for the MEAN is related to the 'standard error', which is:\n",
    "\n",
    "$s_e = \\frac {s}{\\sqrt N}$.\n",
    "\n",
    "\n",
    "The 95% confidence bounds for the mean is given by 1.97$s_e$.  This means in practice that the mean will be more than 1.97$s_e$ away from true mean 5% of the time.    We could test that statement with another little Monte Carlo type simulation, but I leave that to student curiosity.   \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to look at one last distribution:  the log-normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### Log normal\n",
    "\n",
    "Many things in nature are not normally distributed.  Many processes lead to distributions in which the log of the quantity is normally distributed instead of the quantity itself.  For example, grain sizes in sedimentary sequences are often log normally distributed.  These distributions are _log-normal_ and behave differently than normal distributions.  \n",
    "\n",
    "#### Theoretical\n",
    "\n",
    " The equation for the log-normal probability density function is this: \n",
    "\n",
    "$$P=f(x,\\mu, \\sigma)= \\frac{1}{x\\sigma \\sqrt{2\\pi}} \\exp {\\bigl(-\\frac{(\\text{ln}(x)-\\mu)^2}{2\\sigma^2}}\\bigr),0< x < \\infty$$\n",
    "\n",
    "Notice that $x$ is in the denominator so we can't evaluate the probability when $x$=0.  \n",
    "\n",
    "As before we make a **lambda** function  to evaluate the probability density of log-normal distributions:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here is a log normal probability density function maker: \n",
    "LogNormal=lambda x,mu,sigma : (1./(x*sigma*np.sqrt(2.*np.pi)))*np.e**(-((np.log(x)-mu)**2)/(2.*sigma**2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we evaluate it for a range of possible values of $x$ for given $\\mu, \\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate the probability of returning a value x with a normal distribution with mu and sigma\n",
    "mu,sigma,incr=0,.5,.1 # set the mean,  standard deviation and bin width\n",
    "xs=np.arange(incr,4,incr) # make an array of test values\n",
    "Probability=LogNormal(xs,mu,sigma) # get probabilities for the array of Xs\n",
    "plt.bar(xs,Probability,width=incr,color='cyan', edgecolor='k') # make the bar chart\n",
    "plt.plot(xs,Probability,'r-',linewidth=2) # plot as a continuous probability distribution\n",
    "plt.title('Log Normal Distribution')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('Probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Empirical\n",
    "\n",
    "To  simulate data, we can use **random.lognormal( )**, specifying mean and standard deviation as for the normal distribution. \n",
    "\n",
    "Here we plot the theoretical distribution and the  simulated data, along with its mean and the $\\pm \\sigma$ bounds calculated as we did in the last lecture for normal distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu,sigma=0,.5 # set the mean,  standard deviation\n",
    "Nmc=100 # number of monte carlo simultions\n",
    "Simulated=random.lognormal(mu,sigma,Nmc) # get Nmc  simulated data points from distribution\n",
    "plt.bar(xs,Probability,width=incr,color='cyan',edgecolor='k',label='Theoretical') # make the bar chart\n",
    "plt.hist(Simulated,density=True,histtype='step',color='orange',linewidth=3.,label='Simulated') # plot them\n",
    "plt.plot([Simulated.mean(),Simulated.mean()],[0,1],'k-',linewidth=2,label='Mean')\n",
    "plt.plot([Simulated.mean()-Simulated.std(),Simulated.mean()-Simulated.std()],[0,1],\n",
    "        'g--',linewidth=2,label='lower bound')\n",
    "plt.plot([Simulated.mean()+Simulated.std(),Simulated.mean()+Simulated.std()],[0,1],\n",
    "        'r--',linewidth=2,label='upper bound')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hey! \n",
    "\n",
    "Why is the mean way off to the right?  And those confidence bounds don't look right at all!  \n",
    "\n",
    "It turns out that the mean as defined in the last lecture is only good for 'normal' distributions and shouldn't be used for other types. \n",
    "\n",
    "First, let's look at the plot using the log normal of the data instead of the data themselves:  \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "barx=np.log(Simulated).mean() # get the  mean of the logs of the  simulated data set\n",
    "s=np.log(Simulated).std() # get the standard deviation of same\n",
    "plt.hist(np.log(Simulated),density=True,histtype='step',color='orange',linewidth=3) # plot them \n",
    "plt.plot([barx,barx],\\\n",
    "         [0,1],'k-',linewidth=2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "It appears that a log normal distribution looks more \"normal\" when plotted on a log scale.  But the mean doesn't behave the way we expect for normal distributions (offset to the long tail). \n",
    "\n",
    "So what would be a sensible way of describing the _central tendency_ (Expectation $E$) and spread (_variance_)  for a log normal distribution? \n",
    "\n",
    "These are expressed as follows: \n",
    "\n",
    "$$E(x) =\\exp\\bigr( \\mu +\\frac{1}{2}\\sigma^2 \\bigl),$$\n",
    "\n",
    "and \n",
    "\n",
    "$$ \\text{var}(x) = \\bigr[\\exp (\\sigma^2)-1\\bigr]*\\exp(2\\mu + \\sigma^2)$$\n",
    "\n",
    "where $\\mu, \\sigma$ are the mean and standard deviation of the logs of the population.  For the sample, we will refer to them at $\\bar x$ and $s$ respectively and for the expectation and variance we will use $m$ and $v$.  \n",
    "\n",
    "Fortunately, there is a nice **SciPy** package that does statistics for log normal distributions.  **SciPy** is a very powerful package of scientific python functions, many of which were later incorporated into **NumPy**, but not all.  One of the \"leftovers\" is   **scipy.stats.lognorm**.  You can take a look at what **lognorm** can do for us using **help(stats.lognorm)** after we import it, if you are curious.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok - you should be curious!  So let's take a look at the help message: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on lognorm_gen in module scipy.stats._continuous_distns object:\n",
      "\n",
      "class lognorm_gen(scipy.stats._distn_infrastructure.rv_continuous)\n",
      " |  A lognormal continuous random variable.\n",
      " |  \n",
      " |  %(before_notes)s\n",
      " |  \n",
      " |  Notes\n",
      " |  -----\n",
      " |  The probability density function for `lognorm` is:\n",
      " |  \n",
      " |  .. math::\n",
      " |  \n",
      " |      f(x, s) = \\frac{1}{s x \\sqrt{2\\pi}}\n",
      " |                \\exp(-\\frac{1}{2} (\\frac{\\log(x)}{s})^2)\n",
      " |  \n",
      " |  for ``x > 0``, ``s > 0``.\n",
      " |  \n",
      " |  `lognorm` takes ``s`` as a shape parameter.\n",
      " |  \n",
      " |  %(after_notes)s\n",
      " |  \n",
      " |  A common parametrization for a lognormal random variable ``Y`` is in\n",
      " |  terms of the mean, ``mu``, and standard deviation, ``sigma``, of the\n",
      " |  unique normally distributed random variable ``X`` such that exp(X) = Y.\n",
      " |  This parametrization corresponds to setting ``s = sigma`` and ``scale =\n",
      " |  exp(mu)``.\n",
      " |  \n",
      " |  %(example)s\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      lognorm_gen\n",
      " |      scipy.stats._distn_infrastructure.rv_continuous\n",
      " |      scipy.stats._distn_infrastructure.rv_generic\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  fit(self, data, *args, **kwds)\n",
      " |      Return MLEs for shape (if applicable), location, and scale\n",
      " |      parameters from data.\n",
      " |      \n",
      " |      MLE stands for Maximum Likelihood Estimate.  Starting estimates for\n",
      " |      the fit are given by input arguments; for any arguments not provided\n",
      " |      with starting estimates, ``self._fitstart(data)`` is called to generate\n",
      " |      such.\n",
      " |      \n",
      " |      One can hold some parameters fixed to specific values by passing in\n",
      " |      keyword arguments ``f0``, ``f1``, ..., ``fn`` (for shape parameters)\n",
      " |      and ``floc`` and ``fscale`` (for location and scale parameters,\n",
      " |      respectively).\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      data : array_like\n",
      " |          Data to use in calculating the MLEs.\n",
      " |      args : floats, optional\n",
      " |          Starting value(s) for any shape-characterizing arguments (those not\n",
      " |          provided will be determined by a call to ``_fitstart(data)``).\n",
      " |          No default value.\n",
      " |      kwds : floats, optional\n",
      " |          Starting values for the location and scale parameters; no default.\n",
      " |          Special keyword arguments are recognized as holding certain\n",
      " |          parameters fixed:\n",
      " |      \n",
      " |          - f0...fn : hold respective shape parameters fixed.\n",
      " |            Alternatively, shape parameters to fix can be specified by name.\n",
      " |            For example, if ``self.shapes == \"a, b\"``, ``fa``and ``fix_a``\n",
      " |            are equivalent to ``f0``, and ``fb`` and ``fix_b`` are\n",
      " |            equivalent to ``f1``.\n",
      " |      \n",
      " |          - floc : hold location parameter fixed to specified value.\n",
      " |      \n",
      " |          - fscale : hold scale parameter fixed to specified value.\n",
      " |      \n",
      " |          - optimizer : The optimizer to use.  The optimizer must take ``func``,\n",
      " |            and starting position as the first two arguments,\n",
      " |            plus ``args`` (for extra arguments to pass to the\n",
      " |            function to be optimized) and ``disp=0`` to suppress\n",
      " |            output as keyword arguments.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      mle_tuple : tuple of floats\n",
      " |          MLEs for any shape parameters (if applicable), followed by those\n",
      " |          for location and scale. For most random variables, shape statistics\n",
      " |          will be returned, but there are exceptions (e.g. ``norm``).\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      This fit is computed by maximizing a log-likelihood function, with\n",
      " |      penalty applied for samples outside of range of the distribution. The\n",
      " |      returned answer is not guaranteed to be the globally optimal MLE, it\n",
      " |      may only be locally optimal, or the optimization may fail altogether.\n",
      " |      \n",
      " |      When the location parameter is fixed by using the `floc` argument,\n",
      " |      this function uses explicit formulas for the maximum likelihood\n",
      " |      estimation of the log-normal shape and scale parameters, so the\n",
      " |      `optimizer`, `loc` and `scale` keyword arguments are ignored.\n",
      " |      \n",
      " |      Examples\n",
      " |      --------\n",
      " |      \n",
      " |      Generate some data to fit: draw random variates from the `beta`\n",
      " |      distribution\n",
      " |      \n",
      " |      >>> from scipy.stats import beta\n",
      " |      >>> a, b = 1., 2.\n",
      " |      >>> x = beta.rvs(a, b, size=1000)\n",
      " |      \n",
      " |      Now we can fit all four parameters (``a``, ``b``, ``loc`` and ``scale``):\n",
      " |      \n",
      " |      >>> a1, b1, loc1, scale1 = beta.fit(x)\n",
      " |      \n",
      " |      We can also use some prior knowledge about the dataset: let's keep\n",
      " |      ``loc`` and ``scale`` fixed:\n",
      " |      \n",
      " |      >>> a1, b1, loc1, scale1 = beta.fit(x, floc=0, fscale=1)\n",
      " |      >>> loc1, scale1\n",
      " |      (0, 1)\n",
      " |      \n",
      " |      We can also keep shape parameters fixed by using ``f``-keywords. To\n",
      " |      keep the zero-th shape parameter ``a`` equal 1, use ``f0=1`` or,\n",
      " |      equivalently, ``fa=1``:\n",
      " |      \n",
      " |      >>> a1, b1, loc1, scale1 = beta.fit(x, fa=1, floc=0, fscale=1)\n",
      " |      >>> a1\n",
      " |      1\n",
      " |      \n",
      " |      Not all distributions return estimates for the shape parameters.\n",
      " |      ``norm`` for example just returns estimates for location and scale:\n",
      " |      \n",
      " |      >>> from scipy.stats import norm\n",
      " |      >>> x = norm.rvs(a, b, size=1000, random_state=123)\n",
      " |      >>> loc1, scale1 = norm.fit(x)\n",
      " |      >>> loc1, scale1\n",
      " |      (0.92087172783841631, 2.0015750750324668)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from scipy.stats._distn_infrastructure.rv_continuous:\n",
      " |  \n",
      " |  __init__(self, momtype=1, a=None, b=None, xtol=1e-14, badvalue=None, name=None, longname=None, shapes=None, extradoc=None, seed=None)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  cdf(self, x, *args, **kwds)\n",
      " |      Cumulative distribution function of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      cdf : ndarray\n",
      " |          Cumulative distribution function evaluated at `x`\n",
      " |  \n",
      " |  expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)\n",
      " |      Calculate expected value of a function with respect to the\n",
      " |      distribution.\n",
      " |      \n",
      " |      The expected value of a function ``f(x)`` with respect to a\n",
      " |      distribution ``dist`` is defined as::\n",
      " |      \n",
      " |                  ubound\n",
      " |          E[x] = Integral(f(x) * dist.pdf(x))\n",
      " |                  lbound\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      func : callable, optional\n",
      " |          Function for which integral is calculated. Takes only one argument.\n",
      " |          The default is the identity mapping f(x) = x.\n",
      " |      args : tuple, optional\n",
      " |          Shape parameters of the distribution.\n",
      " |      loc : float, optional\n",
      " |          Location parameter (default=0).\n",
      " |      scale : float, optional\n",
      " |          Scale parameter (default=1).\n",
      " |      lb, ub : scalar, optional\n",
      " |          Lower and upper bound for integration. Default is set to the\n",
      " |          support of the distribution.\n",
      " |      conditional : bool, optional\n",
      " |          If True, the integral is corrected by the conditional probability\n",
      " |          of the integration interval.  The return value is the expectation\n",
      " |          of the function, conditional on being in the given interval.\n",
      " |          Default is False.\n",
      " |      \n",
      " |      Additional keyword arguments are passed to the integration routine.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      expect : float\n",
      " |          The calculated expected value.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      The integration behavior of this function is inherited from\n",
      " |      `integrate.quad`.\n",
      " |  \n",
      " |  fit_loc_scale(self, data, *args)\n",
      " |      Estimate loc and scale parameters from data using 1st and 2nd moments.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      data : array_like\n",
      " |          Data to fit.\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information).\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      Lhat : float\n",
      " |          Estimated location parameter for the data.\n",
      " |      Shat : float\n",
      " |          Estimated scale parameter for the data.\n",
      " |  \n",
      " |  isf(self, q, *args, **kwds)\n",
      " |      Inverse survival function (inverse of `sf`) at q of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      q : array_like\n",
      " |          upper tail probability\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      x : ndarray or scalar\n",
      " |          Quantile corresponding to the upper tail probability q.\n",
      " |  \n",
      " |  logcdf(self, x, *args, **kwds)\n",
      " |      Log of the cumulative distribution function at x of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      logcdf : array_like\n",
      " |          Log of the cumulative distribution function evaluated at x\n",
      " |  \n",
      " |  logpdf(self, x, *args, **kwds)\n",
      " |      Log of the probability density function at x of the given RV.\n",
      " |      \n",
      " |      This uses a more numerically accurate calculation if available.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      logpdf : array_like\n",
      " |          Log of the probability density function evaluated at x\n",
      " |  \n",
      " |  logsf(self, x, *args, **kwds)\n",
      " |      Log of the survival function of the given RV.\n",
      " |      \n",
      " |      Returns the log of the \"survival function,\" defined as (1 - `cdf`),\n",
      " |      evaluated at `x`.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      logsf : ndarray\n",
      " |          Log of the survival function evaluated at `x`.\n",
      " |  \n",
      " |  nnlf(self, theta, x)\n",
      " |      Return negative loglikelihood function.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      This is ``-sum(log pdf(x, theta), axis=0)`` where `theta` are the\n",
      " |      parameters (including loc and scale).\n",
      " |  \n",
      " |  pdf(self, x, *args, **kwds)\n",
      " |      Probability density function at x of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      pdf : ndarray\n",
      " |          Probability density function evaluated at x\n",
      " |  \n",
      " |  ppf(self, q, *args, **kwds)\n",
      " |      Percent point function (inverse of `cdf`) at q of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      q : array_like\n",
      " |          lower tail probability\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      x : array_like\n",
      " |          quantile corresponding to the lower tail probability q.\n",
      " |  \n",
      " |  sf(self, x, *args, **kwds)\n",
      " |      Survival function (1 - `cdf`) at x of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      x : array_like\n",
      " |          quantiles\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      sf : array_like\n",
      " |          Survival function evaluated at x\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from scipy.stats._distn_infrastructure.rv_generic:\n",
      " |  \n",
      " |  __call__(self, *args, **kwds)\n",
      " |      Freeze the distribution for the given arguments.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution.  Should include all\n",
      " |          the non-optional arguments, may include ``loc`` and ``scale``.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      rv_frozen : rv_frozen instance\n",
      " |          The frozen distribution.\n",
      " |  \n",
      " |  __getstate__(self)\n",
      " |  \n",
      " |  __setstate__(self, state)\n",
      " |  \n",
      " |  entropy(self, *args, **kwds)\n",
      " |      Differential entropy of the RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information).\n",
      " |      loc : array_like, optional\n",
      " |          Location parameter (default=0).\n",
      " |      scale : array_like, optional  (continuous distributions only).\n",
      " |          Scale parameter (default=1).\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      Entropy is defined base `e`:\n",
      " |      \n",
      " |      >>> drv = rv_discrete(values=((0, 1), (0.5, 0.5)))\n",
      " |      >>> np.allclose(drv.entropy(), np.log(2.0))\n",
      " |      True\n",
      " |  \n",
      " |  freeze(self, *args, **kwds)\n",
      " |      Freeze the distribution for the given arguments.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution.  Should include all\n",
      " |          the non-optional arguments, may include ``loc`` and ``scale``.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      rv_frozen : rv_frozen instance\n",
      " |          The frozen distribution.\n",
      " |  \n",
      " |  interval(self, alpha, *args, **kwds)\n",
      " |      Confidence interval with equal areas around the median.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      alpha : array_like of float\n",
      " |          Probability that an rv will be drawn from the returned range.\n",
      " |          Each value should be in the range [0, 1].\n",
      " |      arg1, arg2, ... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information).\n",
      " |      loc : array_like, optional\n",
      " |          location parameter, Default is 0.\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter, Default is 1.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      a, b : ndarray of float\n",
      " |          end-points of range that contain ``100 * alpha %`` of the rv's\n",
      " |          possible values.\n",
      " |  \n",
      " |  mean(self, *args, **kwds)\n",
      " |      Mean of the distribution.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      mean : float\n",
      " |          the mean of the distribution\n",
      " |  \n",
      " |  median(self, *args, **kwds)\n",
      " |      Median of the distribution.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          Location parameter, Default is 0.\n",
      " |      scale : array_like, optional\n",
      " |          Scale parameter, Default is 1.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      median : float\n",
      " |          The median of the distribution.\n",
      " |      \n",
      " |      See Also\n",
      " |      --------\n",
      " |      stats.distributions.rv_discrete.ppf\n",
      " |          Inverse of the CDF\n",
      " |  \n",
      " |  moment(self, n, *args, **kwds)\n",
      " |      n-th order non-central moment of distribution.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      n : int, n >= 1\n",
      " |          Order of moment.\n",
      " |      arg1, arg2, arg3,... : float\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information).\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |  \n",
      " |  rvs(self, *args, **kwds)\n",
      " |      Random variates of given type.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information).\n",
      " |      loc : array_like, optional\n",
      " |          Location parameter (default=0).\n",
      " |      scale : array_like, optional\n",
      " |          Scale parameter (default=1).\n",
      " |      size : int or tuple of ints, optional\n",
      " |          Defining number of random variates (default is 1).\n",
      " |      random_state : None or int or ``np.random.RandomState`` instance, optional\n",
      " |          If int or RandomState, use it for drawing the random variates.\n",
      " |          If None, rely on ``self.random_state``.\n",
      " |          Default is None.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      rvs : ndarray or scalar\n",
      " |          Random variates of given `size`.\n",
      " |  \n",
      " |  stats(self, *args, **kwds)\n",
      " |      Some statistics of the given RV.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional (continuous RVs only)\n",
      " |          scale parameter (default=1)\n",
      " |      moments : str, optional\n",
      " |          composed of letters ['mvsk'] defining which moments to compute:\n",
      " |          'm' = mean,\n",
      " |          'v' = variance,\n",
      " |          's' = (Fisher's) skew,\n",
      " |          'k' = (Fisher's) kurtosis.\n",
      " |          (default is 'mv')\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      stats : sequence\n",
      " |          of requested moments.\n",
      " |  \n",
      " |  std(self, *args, **kwds)\n",
      " |      Standard deviation of the distribution.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      std : float\n",
      " |          standard deviation of the distribution\n",
      " |  \n",
      " |  var(self, *args, **kwds)\n",
      " |      Variance of the distribution.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      arg1, arg2, arg3,... : array_like\n",
      " |          The shape parameter(s) for the distribution (see docstring of the\n",
      " |          instance object for more information)\n",
      " |      loc : array_like, optional\n",
      " |          location parameter (default=0)\n",
      " |      scale : array_like, optional\n",
      " |          scale parameter (default=1)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      var : float\n",
      " |          the variance of the distribution\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from scipy.stats._distn_infrastructure.rv_generic:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      " |  \n",
      " |  random_state\n",
      " |      Get or set the RandomState object for generating random variates.\n",
      " |      \n",
      " |      This can be either None or an existing RandomState object.\n",
      " |      \n",
      " |      If None (or np.random), use the RandomState singleton used by np.random.\n",
      " |      If already a RandomState instance, use it.\n",
      " |      If an int, use a new RandomState instance seeded with seed.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(stats.lognorm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function **stats.norm** returns 'moments' of data samples,  the first two of which are the log normal mean ($m$) and the variance $v$.\n",
    "\n",
    "So, we should do the following: \n",
    "- calculate the mean $\\bar x$, and standard deviation $s$  of the LOG of the simulated dataset, \n",
    "- set the **scale** to be $e^{\\bar x}$\n",
    "- calculate the first few moments, mean ($m$) and variance ($v$).  \n",
    "\n",
    "Now we can calculate the moments, $m$ and $v$ and compare them to the originals $\\bar x$ and $s$ and the $\\mu$ and $\\sigma$ of the theoretical distribution used to generate the simulated data: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu   0.00  and barx  0.02\n",
      "sigma  0.50  and s  0.50\n",
      "E  1.13  and m  1.16\n",
      "var 0.365         and v  0.379\n"
     ]
    }
   ],
   "source": [
    "m,v=stats.lognorm.stats(s,moments='mv',scale=np.exp(barx))\n",
    "print ('mu  %5.2f'%(mu),' and barx %5.2f'%(barx))\n",
    "print ('sigma %5.2f'%(sigma),' and s %5.2f'%(s))\n",
    "print ('E %5.2f'%(np.exp(mu + 0.5*sigma**2)),' and m %5.2f'%(m))\n",
    "print ('var %5.3f'%((np.e**(sigma**2)-1)*np.e**(2*mu+sigma**2)),' \\\n",
    "       and v  %5.3f'%(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is also a **NumPy** function to calculate the median (**np.median( )**) and  for the mode we can use **scipy.stats.mode( )**.  But be careful with this  because it finds the most frequent value, which may have a bunch of significant figures and so each value occurs only once.  To get a reasonable estimate of the  mode, we first have to round off the numbers in **Simulated**.  We can use **np.round()** for that.  \n",
    "\n",
    "Here's how to calculate each of these types of expected values:  \n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean:  1.156629982755693\n",
      "mean other way:  1.156629982755693\n",
      "median:  1.0814143428971879\n",
      "mode:  [1.2]  count:  [10]\n"
     ]
    }
   ],
   "source": [
    "mean=Simulated.mean() # you knew this already\n",
    "mean_other_way =np.mean(Simulated) # this is a different way, but works the same.  \n",
    "median=np.median(Simulated) # this is the way to do the median with NumPy\n",
    "mode,count=stats.mode(np.round(Simulated,1)) # round to 2 significant digits, return mode and number in that mode\n",
    "print ('mean: ',mean)\n",
    "print ('mean other way: ',mean_other_way)\n",
    "print ('median: ',median)\n",
    "print ('mode: ',mode,' count: ',count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that **mode** and **count** are both lists.   \n",
    "\n",
    "So let's plot up the data and put  the  mean, median and the mode on it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Th1f37uW6zZt5dPTobnlfpeDbM+EjbZaZ1e4+bZXOvvHGG5k0aRKLFy/mnXfeYd68eaxZs4abb76ZI444ghtuuIFXX301uFbChg0beO655/jwww9xu91cdNFFLFiwgHnz5lny+axkZVIYBJSE3C4Fpjfb5ybgTRH5DZAKHGNhPFEvOA01NxdHN6598NcRI3hzxQoe27mTiwYNCqs0t1Kxrq3S2R988AEvvvgiAEcddRTl5eVUVFSwbNkyXnrpJQB+/OMfkxn48fbf//6XVatWMXXqVKBxMZ6+fft246eJHCuTQkt/1ZoXwzkTeMIYc7eIfA/4l4gcZow5aNRTRM4HzgfIy8uzJFi7rams5P2KCtItmobalpEpKVwyaBB3l5Zy25Yt/N9hh3Xr+6ueK5xf9FZqq3R2c03nC7V03pAxhl/+8pfcfvvt1gXbTawcaC4FBofczuW73UPnAc8DGGOWA0lAdvMXMsY8ZIyZYoyZkpOTY1G49vrnjh0AnNu/P+kWTUNty5V5eSQ5HCwuK2N9dXW3v79SdmitdHZoieylS5eSnZ1NRkbGQfe//vrr7Nu3D4Cjjz6aRYsWsXv3bqBxTGLLli3d+Ekix8qksAIYKSLDRCSBxoHkJc322QocDSAiY2hMCnssjClqLd2/H4Azu7mV0KRfQgLn9u8PwJ1bt9oSg1LdrbXS2TfddBMrV64kPz+fa665hieffBJoHGtYtmwZBQUFvPnmm8Gei7Fjx3Lbbbdx3HHHkZ+fz7HHHsuOwA+9WGNp6ezAFNN7ACfwmDHmjyJyC7DSGLMkMBvpYSCNxq6lq4wxb7b1mvFYOrvc4yH7ww9JcjioOOIIEhydyNVhlM5ub9/i2lpGfPIJAEXTpzM0UJlVS2erSNLS2dbrSulsS/spjDGvAa81u++GkO0vgO9bGUMs+PjAAQCmpqd3LiFEyNDkZM7s14+nd+3irpIS7jv0UNtiUUrZQ89ojgIfVVQAcHhGRjt7Wu+aQHP40Z079bwFpXogTQpR4KNAS+H7vXrZHAmMS01lTlYWdX4/fwssBapUpMXaio+xpKvHVpOCzTx+P58GksL3oqClAHBtoLXwj23bqPB6bY5GxZukpCTKy8s1MVjAGEN5eTlJSZ1fQKv75z6qg3xeVUWN38+hyclkJyTYHQ4AM3r14sjevXl3/37u15pIKsJyc3MpLS1lz54eOdHQcklJSeR2oUyOJgWbNXUdHR4FXUehrs3L4939+7mnjS6kppN49Bef6gi3282wwLKwKvpo95HNommQOdQxmZlMTktjt8djdyhKqW6kScFm0dpSEBGuHTLE7jCUUt1Mk4KNSurqKKmvp5fTyRiL107ojJ9mZzMqcAKbUqpn0KRgo+VNs4569erWqqjhcohwdUgBQn+LNQ6VUvFEk4KNonU8IdRZIbWYliQdbmMkSqnuoEnBRtE6nhAqtOzG7Wln6UwjpeKcJgWb1Ph8rK6qwgFMi5FFbT5NGMO7gWquSqn4pEnBJisrK/EaQ35ami3rJ3TWXSUl7e+klIpZmhRsEgvjCc0l++t4fe9evtBFeJSKW7HzEzUaPdP52Tgf9bkNkr7P4et/DSvfbnvnKFmXYH7tGzyQehJ/KSnhkdGj7Q5HKWUBbSnYwAAfuRvXQT68odDeYDrgt1UvIMC/du3SstpKxSlNCjb42plLubMXA3xlDPXttDucsI30bWNOVhYNxvAPLZSnVFzS7qNI6UAXz0c7dsDGjRzebzRydCvP60LXlJWuGDyYl8vLtXqqUnFKWwo2+DAGzk9ozRG9ejE1PZ1yXWdBqbikScEGsTjzqImIcMXgwXaHoZSyiCaFbrbP4+GLmhoSRZgUIyetNXdqdjZDEhPtDkMpZQFNCt3s40DX0ZT0dBIdsXn4XQ4Hl3ZhZSelVPSKzb9KMSwW6h2F47wBA4LbKwOfSSkV+zQpdLNYHk8IlRFSmuPuNpbsVErFFk0K3cjr9/NJyBoK8eKF3bvtDkEpFSGaFLrRuupqqv1+DklKol9Cgt3hRIzP7gCUUhGjSaEbxct4glIqfoV1RrOIHApcCQwJfY4x5iiL4opL8TKe0Nys3r0BXWdBqXgQbpmLF4AHgYfR3oJO63RLIUpLXjS5IjeXpqTgwYlb/4soFbPC7T7yGmMeMMZ8aoxZ1XSxNLI4s72+nuK6OjKcTsalptodTkTNzsoKbj+ffKSNkSiluircpPBvEblIRAaISJ+mi6WRxZnlgVbCjIwMnBLdv/w7yhHyef6cdgbRsfqDUqozwu0++mXg+sqQ+wwwvK0nicjxwN8AJ/CIMeaOFvb5GXBT4PU+N8b8PMyYYkpwPCHcrqMoWVinoz53j+CNxKkcX7/C7lCUUp0QVlIwxgzr6AuLiBP4B3AsUAqsEJElxpgvQvYZCVwLfN8Ys09E+nb0fWLFZ1VVAEyL0XpHHfGntLmaFJSKUWF1H4mIW0QuEZFFgcvFIuJu52nTgCJjzGZjTAPwLHBSs31+BfzDGLMPwBgTt2dBFQbWNT4szsYTmsvwV/FuYgEr3KPsDkUp1Qnhjik8AEwG7g9cJgfua8sgoCTkdmngvlCHAoeKyIci8nGgu+k7ROR8EVkpIiv37NkTZsjRY3dDA2UeDxlOJ7lxXl30wup/A3Bn2pk2R6KU6oxwk8JUY8wvjTHvBC7nAFPbeU5Lo6nNO8pdwEhgFnAm8IiI9P7Ok4x5yBgzxRgzJScnJ8yQo0dTK2FcaioSZ4PMzV1a/SIJpoGXkmbyVU2N3eEopToo3KTgE5FDmm6IyHDaP1+hFAhdjSUX2N7CPi8bYzzGmG+AjTQmibiyvod0HQEM9Jfzi5q3MOLgrpKS9p+glIoq4SaFK4F3RWSpiLwHvANc0c5zVgAjRWSYiCQAc4ElzfZZDBwJICLZNHYnbQ43+FgR2lLoCa6seg4xfp7cuZOd9fV2h6OU6oCwkoIx5r80/oK/JHAZZYx5t53neIGLgTeADcDzxpj1InKLiMwJ7PYGUC4iXwDvAlcaY8o791GiV08ZZG4yylfCyXUf0GAMf9u2ze5wlFId0OaUVBE5yhjzjoic0uyhQ0QEY8xLbT3fGPMa8Fqz+24I2TbA5YFLXDLGBLuPxqWk2BxN97m66ln+L/kHPLBtG9fm5R20/oJSKnq111L4YeD6Jy1cTrQwrrixrb6eCp+PLJcrrsplt2e6ZwM/7NWLCp+Pf25vPpSklIpWbf58M8bcGNi8JTAQHCQiHT6hrSdaH5iB0xNmHjV3VV4e761bx19LS7kkNzdm16RWqicJ91v6Ygv3LYpkIPGqp40nhDqhTx/Gp6ayo6GBp3ftsjscpVQY2kwKIjJaRE4FeonIKSGX+UBSt0QY49b3sJlHoUSEqwY3zkr+89at+E1s1nNSqidpr6Uwisaxg94cPJ5QQGOJCtWOntxSADijb1/yEhPZWFvLkrIyu8NRSrWjvTGFl4GXReR7xpjl3RRT3PAbwxc9uKUA4HY4uGLwYC4tKuLOkhJOys7ucWMrSsWScMcULgwtPyEimSLymEUxxY0tdXVU+/30T0ggy91e/cD4dd6AAfRxufj4wAGWBUqIK6WiU7hJId8YE1yEN1DVdJI1IcWPnnh+QktSnU4uyc0F4JbiYnuDUUq1Kdyk4BCRzKYbgVXX9GykdvT08YRQlw4aRC+nk3f27+e9/fvbf4JSyhbhJoW7gY9E5FYRuRX4CPiTdWHFh9BzFHq63m43vw3MRLrxm2/a2VspZZdwax89BZwG7AJ2A6cYY/5lZWDxQFsKB7ssN5feLhfvVVTw7r59doejlGpB2KeYGmPWA88DLwNVIpJnWVRxwGcMGwJJYawmBQB6uVxcHhhbuLG4GKPnLSgVdcJdjnOOiHwNfAO8BxQDr1sYV8zbVFtLvTEMTkyklxaDC7o0N5dMl4v3Kyp4R8cWlIo64bYUbgVmAF8ZY4YBRwMfWhZVHOjJZzK3JcPl4oqQsQVtLSgVXcJNCp7AOgcOEXEE1lKYaGFcMU/HE1r3m0GD6ONy8eGBA7ytYwtKRZVw+zX2i0gasAxYICK7Aa91YcW+mDlH4ZnuP7s4w+Xid4MHc90333Djymc4puw3LS7o3aafawtDKSuE21I4CagBfgv8B9hEYw0k1QptKbTt4kGDyHK5WJ5wGG8mTrU7HKVUQLtJQUScwMvGGL8xxmuMedIYc288LpsZKQ1+PxtrawEYo0mhRekuF1fmNU5guzF9Pvq7X6no0G73kTHGJyI1ItLLGKOFa8LwdW0tXmMYnpREqtNpdzjf1dGul5ulc89rx68HDuSurz/jk4Sx/CdxGiec+knbT7Chq0upnibc7qM6YJ2IPCoi9zZdrAwslunMo/CkuVxcVfUsEGgt6EwkpWwXblJ4FbiexoHmVSEX1QIdTwjfRTUv09e3lxUJY3ht7167w1Gqx2uz+0hE8owxW40xT3ZXQPGgUFsKYUs1dVxd9SxX9LqIm4qLmd2nj663oJSN2mspLG7aEJGW1mlWLVivLYUOubBmCf18e1lZWcnLujqbUrZqLymE/mQbbmUg8aLO56OothYHMCo52e5wYkKKqee6qgUAXLV5Mw1+v80RKdVztZcUTCvbqhVf1tTgB0YmJ5MUjTOPotSF1UsYmZzM17W1PLB9u93hKNVjtZcUJojIARGpBPID2wdEpFJEDnRHgLFGxxM6JwEvdx1yCAA3Fxez1+OxOSKleqY2k4IxxmmMyTDGpBtjXIHtptsZ3RVkLGlaWEfHEzruJ1lZHNW7N/u8Xm7WZTuVskXY6ymo8GhLofNEhL+MGIEA92/fzsZAglVKdR9NChGmM4+6ZkJaGucNGIDXGH63aZPd4SjV42hSiKAqr5dv6upwizBSZx512q1Dh5LmdPJKeTlv6wltSnUrS5OCiBwvIhtFpEhErmljv9NExIjIFCvjsdqGQHfHqJQU3A7Nt53VPzGR6wLF8i7ftAmflr9QqttY9pcrUF31H8AJwFjgTBEZ28J+6cAlQDvV0KJfYaysoRADfpuby5DERNZVV/PYjh12h6NUj2Hlz9lpQJExZrMxpgF4lsZ1GZq7FfgTjUX3YpqOJ0ROktPJnYEpqn/45hsOeHVNJ6W6g5VJYRBQEnK7NHBfkIhMAgYbY16xMI5uozOPIutnOTkcnpHBbo+H27dutTscpXoEK5NCS1XNgp3DIuIA/gpc0e4LiZwvIitFZOWePXsiGGJk6TkKkdU0RRXgryUlFDv72RyRUvHPyqRQCgwOuZ0LhNYvSAcOA5aKSDEwA1jS0mCzMeYhY8wUY8yUnJwcC0PuvP0eD6X19SQ5HAzXmUcRMz0jg5/37Uu9MVydcYHd4SgV96xMCiuAkSIyTEQSgLnAkqYHjTEVxphsY8xQY8xQ4GNgjjFmpYUxWeaLQCthTEoKTi39HFG3Dx9OksPB88lH8n7CeLvDUSquWZYUjDFe4GLgDWAD8LwxZr2I3CIic6x6X7voeIJ18pKSuGpwY6Pz/F5XUIfb5oiUil/trtHcFcaY14DXmt13Qyv7zrIyFqvpzCNrXZuXx/NFy/jSPYRb0+fxR7sDUipO6RlWEbJOz1GwVJLTySMVdyHGz51pZ7KmstLukJSKS5oUIsAAa6uqgMbaPcoa328o5OLqxfjEybkbN+LRxXiUijhNChGww5FFuddLb5eL3MREu8OJa/9b+TBDvDtZXVXF3SUl7T9BKdUhmhQiYK27caXS/NRUXXTeYmmmjocq7gbgpuJiLa+tVIRZOtDcU6x1N5ZjyNeuo4M9Y02CPK5+JefUvM7jKSdw3vuPsqz8UhyRXC3251qAT/Vc2lKIgLWub1sKqnvcXXE//X3lfJg4nvtTWiqppZTqDE0KERDsPtKWQrfJNFXcX3EPANdknK8lMJSKEO0+6qIGXGxwDUHQ6aiAtV0vzV77p8Dp69fzwp49XDD6Df6Tn9/5MR2LurqUijXaUuiiL115eMXFIcnJpLk0x3a3v48cSR+Xizf37ePJnTvtDkepmKdJoYtCZx6p7tcvIYF7ApVUf7tpEzvq622OSKnYpkmhi3Tmkf3O7teP4/v0Yb/Xy9kbNujynUp1gSaFLtKZR/YTER4dNYq+bjfv7N/PLcXFdoe66aLCAAAT40lEQVSkVMzSpNBF69zDAG0p2G1gYiLPjB2LALdu2cKbe/faHZJSMUmTQheUOTLY7swh1V/LsKQku8Pp8Y7OzOTmoUMxwFkbNlBaF/PLfivV7TQpdMG6QNfReO9mHFreIir8fsgQjsvMpMzj4YwvvtCieUp1kCaFLggOMns22xyJauIQ4ekxYxiUkMBHBw5w7Wb9t1GqIzQpdEFwkFmTQlTJSUjguXHjcAJ3l5byclmZ3SEpFTM0KXRB8BwF7yabI1HNfb9XL+48pLEl98sNG9hcW2tzRErFBk0KneQzhsLAzKPx2lKISpfn5nJSVhYVPh+nr19Pnc9nd0hKRT1NCp1UVFtLnSSS591Jb1NtdziqBSLC46NHMywpic+qqrh8k7bolGqPJoVOalp+M9+rrYRolul288K4cSSI8MD27Ty+Y4fdISkV1TQpdNLa6sbWgQ4yR7/J6en8feRIAH61cSOvl5fbHJFS0UuTQicFWwqaFGLC+QMHck1eHj7gtPXr+fTAAbtDUioqaVLopGBLQWcexYz/HTaMef36UeP38+N16/ha13dW6js0KXRChddLcV0diaaBkd5Su8NRYRIRHhk1iuP79KHM4+FHa9eyU0ttK3UQTQqdUBhoJYzzFONCyyjEErfDwQtjxzI1PZ1v6uqYvW4dB7xeu8NSKmpoUuiEb2ceaddRLEpzuXh1/HhGJCezuqqKU9evp0FXplUK0KTQKTrzKPblJCTwRn4+/dxu3t63j3N6X40fLWqolCaFTtCZR/FheHIyr+Xnk+Z08kzKMVyVcYHdISllO00KHeQ3hnU68yhuFKSn89K4cbiNh7vTzuDG9PkYXc5T9WCaFDpoS10dlT4f/RMSyPFX2B2OioBj+/ThqX234zA+bkn/JZcVFeHXxKB6KEtH10TkeOBvgBN4xBhzR7PHLwf+H+AF9gDnGmO2WBlTVwXHE3RN5rgyt+5dEvZ5OTPzD9y7bRsVXi+PjBqFy9HK76ZnOjn+8HNNNiq6WdZSEBEn8A/gBGAscKaIjG2222pgijEmH1gE/MmqeCIlOJ6gazLHnVPq3ueVvdeR4nDw5K5dnP7FF1pZVfU4VnYfTQOKjDGbjTENwLPASaE7GGPeNcY0nVb6MZBrYTwRoS2F+HZs/SrenjCB3i4Xi8vKOHHdOqr0PAbVg1jZfTQIKAm5XQpMb2P/84DXW3pARM4HzgfIy8uLVHydoi2F+Pe9Xr14b+JEjvv8c/67fz/HfP45r+Xn08ftbvkJ7XUJdbarSSkbWNlSaOmb0OK3R0TOBqYAf27pcWPMQ8aYKcaYKTk5OREMsWNqfD6+rq3FJcLolBTb4lDWy09L4/1JkxiSmMgnlZX8cM0admhJDNUDWJkUSoHBIbdzge3NdxKRY4DfA3OMMVH9rVtfXY0BRqekkNjaAKSKGyNTUvhg0iRGp6RQWF3NzNWrtYieintW/mVbAYwUkWEikgDMBZaE7iAik4B/0pgQdlsYS0Q0jSeM1/GEHiM3KYllEydSkJbGpro6pqxaxctlZXaHpZRlLEsKxhgvcDHwBrABeN4Ys15EbhGROYHd/gykAS+IyBoRWdLKy0WF4HiCJoUeJSchgXcnTuSU7GwO+HycXFjI79PPw6en+ag4ZOl5CsaY14DXmt13Q8j2MVa+f6QFZx7pIHOPk+FysWjcOO4qKeGazZv53/Sz+TRhNAv33Uq23cEpFUH6UydMxhhtKfRwIsKVeXm8NWECOb59vJ04hYLsh3QVNxVXNCmEaXtDA3u9XjJdLgYlJtodjrLRUZmZfLbnfKY3fEGJqx8zV6/moe3btWaSiguaFMIU2koQ0XnnPV2uv4z3yi7jourFNBjDBV99xXkbN1KjZ0CrGKdJIUw6nqCaS8TDPyr+xlOjR5PscPD4zp3kr1jBu/v22R2aUp2mSSFMqysrAR1PUN/1i/79WV5QwPjUVDbV1XHU559zwcaNVGh5DBWDdA3CMDT4/fxn714AftC7t83RKMt1oizFhLQ0Vk6ezJ1bt3Lrli08tGMHr5SX88ChhzIndMeOvna0lNDQ6q49hrYUwvDOvn1U+HyMT03lUC1voVqR4HBw/dChrJ4yhRkZGWxvaOCkwkLmZl7Pbof+mFCxQZNCGBbt2QPAqTbWXVKxY1xqKh9MmsTfRowgxeHgueSjGNP3CZ5OPqbl4l9KRRHtPmqH1+9ncaCswWmaFOJXhLtHnCJckpvLT7KyuOCrr3hrH/wi8/c8OORO7hg+nCPa6oaMlgV8tLprj6QthXa8V1FBudfLqORkxmrXkeqgYcnJvJGfz+OjRpHtdvPhgQPMXLOGOevWURiY5qxUNNGk0I6mrqPTcnL0/ATVKSLC/AED2DR9OjcMGUKqw8G/y8vJX7mSc778kq11dXaHqFSQJoU2+Izh/0KSglJdkeFycfOwYWyaMYNfDxyIU4Qndu7k0E8+4XdFRZR7PHaHqJQmhbZ8WFHBLo+H4UlJTNCT1lSE9EtI4L5DD2XD1KnM7duXemO4u7SU4R9/zLWbN7PNoSX2lH00KbRBu46UlUakpLBw7FhWTZ7MsZmZHPD5uGPrVob2W8jZva/jM/dIu0NUPZAmhVb4jeEl7TpS3aAgPZ03J0zgo0mTOD0nBz/CgpRjmZzzELNWr+blsjJ8WmxPdRNNCq345MABtjU0kJeYyJT0dLvDUT3A93r14vlx49i0+ywur3qedH8171VUcHJhIaM//ZT7Sku1dIaynCaFVrwYcsKadh2p7jTUt4u7DzxA6a6f8ddDDmFoUhJFtbX8pqiI/h99xNz163m1vByP3293qCoOaVJogTFGz2JWtsswNVw2eDBfT5vGC2PHcmTv3tT7/Ty3Zw8nrltH7vLl/DbjIla7RuiZ0ipi9IzmFqyqrGRLfT0DEhL4XkaG3eGoHs7lcHBa376c1rcvW+vqWLBrF0/t2sWXNTXck3Y696SdzjjPN8zbupVTc3I4JDnZ7pBVDNOk0IIXA2UtTs3JwaFdR8pOzUpN5AHXAtcAq9yH8lTyj1iYfBTr3cO4evNmrt68mTEpKczJyuIn2dnMyMjAGQ//h6Ol9EcPoEmhmYO6jrJ1vriKTgJM8XzFFM9X3HXgAf6TOI2FYx7m9fJyNtTUsKGmhjtLSsh2u5ndpw9zsrM5LjOTdJd+5VXb9H9IM+uqqymqrSXH7Wamrp2gYkACXubUf8ScsWPx+P18UFHBkvJy/l1Wxqa6Op4KdDe5RZiRkcGs3r2Z1bs338vIINnptDt8FWU0KTTT1Er4aXZ2fDS7VezpQpeH2+HgyMxMjszM5C+HHMKGmhr+HUgQHx04wPsVFbxfUcGtW7aQIML0kCQxIyODlFhIEtGy8FCc0qTQzCI9YU3FCRFhbGoqY1NTuTovj30eD+9XVLB0/36W7t/Pmqqqg5KEW4T81FSmZmQwNT2dqa5hjPFuwYVOfe1JNCmE+KK6mg01NfRxuZilXUcqzmS63czJzmZOYKxsn8fDByFJYnVVFasClwcB+j5Gir+WSZ4iphYVMSU9nfzUVEalpJDg0Nns8UqTQoimE9ZOys7Grf/pVZzLdLv5SXY2PwkkiQNeL59VVrKyspIVlZWs2PE537gG8mHieD4sLQ0+zwkcmpLCuNRUDktNZVxKCoelpjIiORmXfm9iniaFEC9q15HqwTJcLmZlZjIrM7Pxjs8Po8yRwSr3KFZMfp5VVVUUVlezqbY2OMOpqbsVIEGE4cnJjGjhMiQxURNGjNCkEPB1TQ2fV1eT4XRydNOXQqkeLtt/gB/Vr+BHQ4cG76vx+fiypob11dUUVlcHr7fU1/NlTQ1f1tR853VcIgxJTGRoUhKDk5LIS0wkL+R6cGJibAxy9wCaFGg8N+GhHTsAmJOdTaL+olGqVSlOJwXp6RQ0KxRZ5fWyua6Ootra71xK6uvZVFfHpjZWmctyuRiQmMiAhAQGJCTQP3A9IDGR/gkTGOArJ8e/n97GaD0yC/X4pLBs/36u3LSJTysrAfh53742R6RUbEpzuchPSyO/hQWpan0+vqmro6S+nq11dWwNXJeEXJd7vZR7vRRWV3/3xbPvCW66li0jy+Ui2+0mJyGh8drtJtvtJtPlIjP5R2SaKjL9lWRWVTXe53aT4nBoMgmDpUlBRI4H/kbj2NQjxpg7mj2eCDwFTAbKgTOMMcVWxtRkQ3U112zezJLycgD6JyRw27BhnJCV1R1vr1SPkux0BqfHtsRvDLsbGtjZ0MCOwCW4XV/Pzm3vssPZhzJHLw440tjl8bDL44EWuqrIvObb7ZUrg5sJImS4XGQ4nfQKXGc0u04LuaS2cDvV6STF4SDZ4SDZ6YzLc5ksSwoi4gT+ARwLlAIrRGSJMeaLkN3OA/YZY0aIyFzgTuAMq2IC2Flfz03FxTyyYwc+INXh4Kq8PC7PzSVNSwAoZQuHCP0TE+mfmMjElnZYOz64WT/XR7nHwx6PhzKPhz0NDY3XHg/7vF72ff04+xzp7HOks7/3tMb7vF7q/H7KAs+JlEQRUgKJIsXpJMnhCF6SQ7abLolNFxESQrab7k8I3J8ggrvZ7QSHgyyXi6EWFzy08q/gNKDIGLMZQESeBU4CQpPCScBNge1FwH0iIsZEfpmpKq+Xu0tL+fPWrVT7/TiBCwcO5MYhQ+ifmBjpt1NKWSTR4WBgYiIDW/verrj92+3jvv1TUufzccDn44DXe9B1RcjtKp+PKp+P6sB180uN30+t309NYLveGOq9XvZZ/Jmb/Cwnh+fGjbP0PaxMCoOAkpDbpcD01vYxxnhFpALIAsoiGYjfGGZ89hnrA03NOVlZ3DF8OGNaacoqpZqJg9IRSU4nSU4nfRMSIvJ6xhjqmiWJusClNmQ7eJ/P15hE/P5vL8bQ0GzbE7huCLluum94N5RFtzIptPS/qHkLIJx9EJHzgfMDN6tEZGMr75lNGAllSeASUWeF9aUJKz4btRmf3NTyZzxo8M7avx0xffyiRLTH2H584X3XOr5veGw9fp8Bd7S9S1vxDQnnPaxMCqXA4JDbucD2VvYpFREX0AvY2/yFjDEPAQ+194YistIYM6XTEVtM4+saja/roj1Gja9rIhGflRPyVwAjRWSYiCQAc/nuD/QlwC8D26cB71gxnqCUUio8lrUUAmMEFwNv0Dgl9TFjzHoRuQVYaYxZAjwK/EtEimhsIcy1Kh6llFLts3QOpjHmNeC1ZvfdELJdB5wewbdst4vJZhpf12h8XRftMWp8XdPl+ER7a5RSSjXRIj9KKaWCYjIpiMjxIrJRRIpE5JoWHk8UkecCj38iIkOjLL75IrJHRNYELv+vm+N7TER2i0hhK4+LiNwbiH+tiBREWXyzRKQi5Pjd0NJ+FsU2WETeFZENIrJeRC5tYR/bjl+Y8dl5/JJE5FMR+TwQ380t7GPb9zfM+Gz9/gZicIrIahF5pYXHunb8jDExdaFx0HoTMBxIAD4Hxjbb5yLgwcD2XOC5KItvPnCfjcfwB0ABUNjK47OB12k862AG8EmUxTcLeMWmYzcAKAhspwNftfDva9vxCzM+O4+fAGmBbTfwCTCj2T52fn/Dic/W728ghsuBZ1r6d+zq8YvFlkKwfIYxpgFoKp8R6iTgycD2IuBo6b7yiOHEZytjzDJaOB8kxEnAU6bRx0BvERnQPdGFFZ9tjDE7jDGfBbYrgQ00npkfyrbjF2Z8tgkck6rATXfg0nxg07bvb5jx2UpEcoEfA4+0skuXjl8sJoWWymc0/09/UPkMoKl8RncIJz6AUwNdC4tEZHALj9sp3M9gp+8Fmvivi4i1xWBaEWiWT6Lx12SoqDh+bcQHNh6/QNfHGmA38JYxptXjZ8P3N5z4wN7v7z3AVYC/lce7dPxiMSlErHyGRcJ5738DQ40x+cDbfJvVo4Wdxy8cnwFDjDETgL8Di7s7ABFJA14ELjPGHGj+cAtP6dbj1058th4/Y4zPGDORxioH00TksGa72Hr8wojPtu+viJwI7DbGrGprtxbuC/v4xWJS6Ej5DKSN8hkWaTc+Y0y5MaY+cPNhGteTiCbhHGPbGGMONDXxTeO5MG4Rye6u9xcRN41/cBcYY15qYRdbj1978dl9/ELi2A8sBY5v9pCd39+g1uKz+fv7fWCOiBTT2DV9lIg83WyfLh2/WEwK0V4+o934mvUvz6Gx3zeaLAHmBWbRzAAqjDE77A6qiYj0b+ojFZFpNP4/Lu+m9xYaz8TfYIz5Syu72Xb8wonP5uOXIyK9A9vJwDHAl812s+37G058dn5/jTHXGmNyjTFDafzb8o4x5uxmu3Xp+MXcqjImystnhBnfJSIyB/AG4pvfXfEBiMhCGmegZItIKXAjjQNqGGMepPEs9NlAEVADnBNl8Z0G/I+IeIFaYG43Jv3vA78A1gX6nQGuA/JC4rPz+IUTn53HbwDwpDQuwuUAnjfGvBIt398w47P1+9uSSB4/PaNZKaVUUCx2HymllLKIJgWllFJBmhSUUkoFaVJQSikVpElBKaVUkCYFpZRSQZoUlFJKBWlSUKqLRGRqoDhakoikBurwN6+Xo1RM0JPXlIoAEbkNSAKSgVJjzO02h6RUp2hSUCoCAnWuVgB1wOHGGJ/NISnVKdp9pFRk9AHSaFztLMnmWJTqNG0pKBUBIrKExlLGw4ABxpiLbQ5JqU6JuSqpSkUbEZkHeI0xzwSqa34kIkcZY96xOzalOkpbCkoppYJ0TEEppVSQJgWllFJBmhSUUkoFaVJQSikVpElBKaVUkCYFpZRSQZoUlFJKBWlSUEopFfT/AXf0S9+YoQqmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "newmode=mode[0] # make this a single number, not a list with one element\n",
    "plt.hist(Simulated,density=True,bins=20,histtype='step',color='orange',linewidth=3) # plot them \n",
    "plt.plot(xs,Probability,'c-',linewidth=2,label='Probability'); # plot the theoretical probability distribution function\n",
    "plt.plot([mean,mean],[0,.75],'k-',linewidth=2,label='Mean') # put on green line, label for legend. \n",
    "plt.plot([median,median],[0,1],'g-',linewidth=2,label='Median') # black line\n",
    "plt.plot([newmode,newmode],[0,1],'m-',linewidth=2,label='Mode') # magenta line\n",
    "plt.legend()   \n",
    "plt.ylim(0,1.1)\n",
    "plt.xlabel('x'); # set the y axis limits.  \n",
    "plt.ylabel('Fraction');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}