Binomial probability mass function python

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.

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].

Examples

>>> 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