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

scipy.stats.bernoulli = <scipy.stats._discrete_distns.bernoulli_gen object>[source]#

A Bernoulli discrete random variable.

As an instance of the rv_discrete class, bernoulli 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 bernoulli is:

\[\begin{split}f(k) = \begin{cases}1-p &\text{if } k = 0\\ p &\text{if } k = 1\end{cases}\end{split}\]

for \(k\) in \(\{0, 1\}\), \(0 \leq p \leq 1\)

bernoulli takes \(p\) as shape parameter, where \(p\) is the probability of a single success and \(1-p\) is the probability of a single failure.

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

Examples

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

Calculate the first four moments:

p = 0.3 mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk')

Display the probability mass function (pmf):

x = np.arange(bernoulli.ppf(0.01, p), ... bernoulli.ppf(0.99, p)) ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf') ax.vlines(x, 0, bernoulli.pmf(x, p), 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 = bernoulli(p) 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 = bernoulli.cdf(x, p) np.allclose(x, bernoulli.ppf(prob, p)) True

Generate random numbers:

r = bernoulli.rvs(p, size=1000)

Methods