Term Entry numpy.random.poisson()

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

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+---
+Title: '.poisson()'
+Description: 'Returns random integers from a Poisson distribution.'
+Subjects:
+  - 'Data Science'
+  - 'Data Visualization'
+Tags:
+  - 'Data Distributions'
+  - 'NumPy'
+  - 'Probability'
+  - 'Random'
+CatalogContent:
+  - 'learn-python-3'
+  - 'paths/data-science-foundations'
+---
+
+NumPy’s `random` module includes the **`.poisson()`** function, which draws random samples from a Poisson distribution. This distribution models the probability of observing `k` events in a fixed time interval, given they occur at a constant average rate $`\lambda`$ and independent of the time since the last event.
+
+**The Poisson distribution**:
+
+$$f\left(k;\lambda\right) = \frac{\lambda^k e^{-\lambda}}{k!}$$
+
+## Syntax
+
+```pseudo
+numpy.random.poisson(lam=1.0, size=None)
+```
+
+**Parameters:**
+
+- `lam` (float, or array_like of floats): The expected number of events occurring over a fixed-time period. Must be `>=0`.
+- `size` (int, or tuple of ints, optional): Specifies the output shape. For example, `(3, 4)` produces a _3×4_ array. If `None`, a single sample is returned if `lam` is scalar; otherwise, `np.array(lam).size` samples are drawn.
+
+**Return value:**
+
+- `out` (ndarray or scalar): Samples drawn from the Poisson distribution with the specified parameters.
+
+## Example 1
+
+This example draws 10 samples from a Poisson distribution with `lam=5`:
+
+```py
+import numpy as np
+
+# Generate 10 random samples from a Poisson distribution with λ = 5
+results = np.random.poisson(5, 10)
+
+# Print the samples
+print(results)
+```
+
+This code outputs something similar to this:
+
+```shell
+[ 7  5 13  5  4  3  2  8  3  4]
+```
+
+## Example 2
+
+This example generates a _3×4_ matrix of random integers from a Poisson distribution with `λ = 5`:
+
+```py
+import numpy as np
+
+# Generate a 3x4 array of Poisson samples with λ = 5
+results = np.random.poisson(5, (3, 4))
+
+print(results)
+```
+
+This code produces 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
+
+This codebyte example generates 10 Poisson-distributed random samples using a lambda value of `5` and prints the result:
+
+```codebyte/python
+import numpy as np
+
+# Set lambda value
+lam = 5
+
+# Set sample size
+size = 10
+
+# Generate samples
+results = np.random.poisson(lam, size)
+
+# Print the samples
+print(results)
+```