scipy.stats.poisson — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.poisson = <scipy.stats._discrete_distns.poisson_gen object>[source]#

A Poisson discrete random variable.

As an instance of the rv_discrete class, poisson object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

Notes

The probability mass function for poisson is:

\[f(k) = \exp(-\mu) \frac{\mu^k}{k!}\]

for \(k \ge 0\).

poisson takes \(\mu \geq 0\) as shape parameter. When \(\mu = 0\), the pmf method returns 1.0 at quantile \(k = 0\).

The probability mass function above is defined in the “standardized” form. To shift distribution use the loc parameter. Specifically, poisson.pmf(k, mu, loc) is identically equivalent to poisson.pmf(k - loc, mu).

Examples

import numpy as np from scipy.stats import poisson import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

mu = 0.6 mean, var, skew, kurt = poisson.stats(mu, moments='mvsk')

Display the probability mass function (pmf):

x = np.arange(poisson.ppf(0.01, mu), ... poisson.ppf(0.99, mu)) ax.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf') ax.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pmf:

rv = poisson(mu) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, ... label='frozen pmf') ax.legend(loc='best', frameon=False) plt.show()

Check accuracy of cdf and ppf:

prob = poisson.cdf(x, mu) np.allclose(x, poisson.ppf(prob, mu)) True

Generate random numbers:

r = poisson.rvs(mu, size=1000)

Methods