scipy.stats.betanbinom#
- scipy.stats.betanbinom = <scipy.stats._discrete_distns.betanbinom_gen object>[source]#
- A beta-negative-binomial discrete random variable. - As an instance of the - rv_discreteclass,- betanbinomobject inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.- See also - betabinom
- Beta binomial distribution 
 - Notes - The beta-negative-binomial distribution is a negative binomial distribution with a probability of success p that follows a beta distribution. - The probability mass function for - betanbinomis:\[f(k) = \binom{n + k - 1}{k} \frac{B(a + n, b + k)}{B(a, b)}\]- for \(k \ge 0\), \(n \geq 0\), \(a > 0\), \(b > 0\), where \(B(a, b)\) is the beta function. - betanbinomtakes \(n\), \(a\), and \(b\) as shape parameters.- References - The probability mass function above is defined in the “standardized” form. To shift distribution use the - locparameter. Specifically,- betanbinom.pmf(k, n, a, b, loc)is identically equivalent to- betanbinom.pmf(k - loc, n, a, b).- Added in version 1.12.0. - Examples - >>> import numpy as np >>> from scipy.stats import betanbinom >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) - Calculate the first four moments: - >>> n, a, b = 5, 9.3, 1 >>> mean, var, skew, kurt = betanbinom.stats(n, a, b, moments='mvsk') - Display the probability mass function ( - pmf):- >>> x = np.arange(betanbinom.ppf(0.01, n, a, b), ... betanbinom.ppf(0.99, n, a, b)) >>> ax.plot(x, betanbinom.pmf(x, n, a, b), 'bo', ms=8, label='betanbinom pmf') >>> ax.vlines(x, 0, betanbinom.pmf(x, n, a, b), 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 = betanbinom(n, a, b) >>> 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 - cdfand- ppf:- >>> prob = betanbinom.cdf(x, n, a, b) >>> np.allclose(x, betanbinom.ppf(prob, n, a, b)) True - Generate random numbers: - >>> r = betanbinom.rvs(n, a, b, size=1000) - Methods - rvs(n, a, b, loc=0, size=1, random_state=None) - Random variates. - pmf(k, n, a, b, loc=0) - Probability mass function. - logpmf(k, n, a, b, loc=0) - Log of the probability mass function. - cdf(k, n, a, b, loc=0) - Cumulative distribution function. - logcdf(k, n, a, b, loc=0) - Log of the cumulative distribution function. - sf(k, n, a, b, loc=0) - Survival function (also defined as - 1 - cdf, but sf is sometimes more accurate).- logsf(k, n, a, b, loc=0) - Log of the survival function. - ppf(q, n, a, b, loc=0) - Percent point function (inverse of - cdf— percentiles).- isf(q, n, a, b, loc=0) - Inverse survival function (inverse of - sf).- stats(n, a, b, loc=0, moments=’mv’) - Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). - entropy(n, a, b, loc=0) - (Differential) entropy of the RV. - expect(func, args=(n, a, b), loc=0, lb=None, ub=None, conditional=False) - Expected value of a function (of one argument) with respect to the distribution. - median(n, a, b, loc=0) - Median of the distribution. - mean(n, a, b, loc=0) - Mean of the distribution. - var(n, a, b, loc=0) - Variance of the distribution. - std(n, a, b, loc=0) - Standard deviation of the distribution. - interval(confidence, n, a, b, loc=0) - Confidence interval with equal areas around the median.