scipy.stats.binom

scipy.stats.binom = <scipy.stats._discrete_distns.binom_gen object>

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.

Methods

rvs(n, p, loc=0, size=1, random_state=None)	Random variates.
pmf(k, n, p, loc=0)	Probability mass function.
logpmf(k, n, p, loc=0)	Log of the probability mass function.
cdf(k, n, p, loc=0)	Cumulative distribution function.
logcdf(k, n, p, loc=0)	Log of the cumulative distribution function.
sf(k, n, p, loc=0)	Survival function (also defined as 1 - cdf, but sf is sometimes more accurate).
logsf(k, n, p, loc=0)	Log of the survival function.
ppf(q, n, p, loc=0)	Percent point function (inverse of cdf — percentiles).
isf(q, n, p, loc=0)	Inverse survival function (inverse of sf).
stats(n, p, loc=0, moments=’mv’)	Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
entropy(n, p, loc=0)	(Differential) entropy of the RV.
expect(func, args=(n, p), loc=0, lb=None, ub=None, conditional=False)	Expected value of a function (of one argument) with respect to the distribution.
median(n, p, loc=0)	Median of the distribution.
mean(n, p, loc=0)	Mean of the distribution.
var(n, p, loc=0)	Variance of the distribution.
std(n, p, loc=0)	Standard deviation of the distribution.
interval(confidence, n, p, loc=0)	Confidence interval with equal areas around the median.

See also

hypergeom, nbinom, nhypergeom

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 isf methods. [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

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

Try it in your browser!

>>> 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)

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