Python:NumPy .poisson()

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

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:

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)

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This code outputs something similar to this:

[ 7  5 13  5  4  3  2  8  3  4]

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Example 2

This example generates a 3×4 matrix of random integers from a Poisson distribution with λ = 5:

import numpy as np

# Generate a 3x4 array of Poisson samples with λ = 5
results = np.random.poisson(5, (3, 4))

print(results)

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This code produces an output similar to this:

[[4 4 4 7]
 [1 8 3 4]
 [3 4 8 5]]

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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:

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