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

scipy.stats.binom = <scipy.stats._discrete_distns.binom_gen object>[source]#

A binomial discrete random variable.

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

\[f(k) = \binom{n}{k} p^k (1-p)^{n-k}\]

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

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

This distribution uses routines from the Boost Math C++ library for the computation of the pmf, cdf, sf, ppf and isfmethods. [1]

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

References

Examples

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

Calculate the first four moments:

n, p = 5, 0.4 mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')

Display the probability mass function (pmf):

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

Generate random numbers:

r = binom.rvs(n, p, size=1000)

Methods