Term Entry numpy.random.poisson()

content/numpy/concepts/random-module/terms/poisson/poisson.md

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+---
+Title: '.poisson()' 
+Description: 'Draw random samples from a Poisson distribution' 
+Subjects: 
+  - 'Data Science'
+  - 'Data Visualization'
+Tags: 
+  - 'Data Distributions'
+  - 'Probability'
+  - 'NumPy'
+  - 'Random'
+CatalogContent: 
+  - 'learn-python-3'
+  - 'learn/intro-statistics-numpy'
+  - 'paths/analyze-data-with-python'
+---
+
+The `random` module for NumPy has a variety of functions to model statistical distributions including the **`.poisson()`** method which randomly draws samples from a Poisson distribution. The Poisson distribution illustrates the probability of `k` events happening over a fixed interval of time given the events occur with a known constant mean rate $`\lambda`$ and independently of time since last event occured. 
+
+**The Poisson distribution**:
+
+$$f\left(k;\lambda\right) eq \frac{\lambda^k e^{-\lambda}}{k!}$$
+
+## Syntax
+
+```pseudo
+numpy.random.poisson(lam=1.0, size=None)
+```
+
+**Parameters**
+- `lam` *float, or array_like of floats*: The expected number of events occuring over a fixed-time period. Must be non-negative.
+- `size` *int, or tuple of ints, (optional)*: Output shape. For example, the tuple `(3, 4)` will output a ndarray with shipe 3 x 4.  If `size=None`, the default argument, then a single sample is drawn if `lam` is scalar, otherwise `np.array(lam).size` samples are drawn.
+
+**Returns**
+- `Out` *ndarray or scalar*: Drawn samples from Poisson distribution given parameter inputs.
+
+## Examples of Generating Random Values From a Poisson Distribution
+
+**Example 1**: Drawing a scalar of random samples from a Poisson distribution with `lam` input of 5
+
+```py
+import numpy as np
+
+# Generate 10 random samples from a Poisson distribution given a lambda input of 5
+result = np.random.poisson(5, 10)
+# Print results to view random sampling
+print(results)
+```
+
+This code will output something similar to this:
+
+```shell
+[ 7 10  5  4  7  5  4  4  2 13]
+```
+
+**Example 2**: Drawing a tuple of random samples from a Poisson distribution with `lam` input of 5
+
+```py
+import numpy as np
+
+# Generate 3 sets of 4 random samples
+results = np.random.poisson(5, (3, 4))
+
+print(results)
+```
+
+This code will produce an output similar to this:
+
+```shell
+[[4 4 4 7]
+ [1 8 3 4]
+ [3 4 8 5]]
+ ```
+
+> [!NOTE]
+> The method produces random results so outcomes will vary.
+
+
+## Codebyte Example 
+
+Below is a codebyte example with the same parameter inputs as Example 1 that allows for experimenting with different parameters.
+
+```codebyte/python
+import numpy as np
+
+# Set lambda value
+lambda = 5
+
+# Set sample size value
+size = 10
+
+# Generate samples and save to a variable
+results = np.random.poisson(lambda, size)
+
+# Print results for viewing
+print(results)
+```