`scipy.stats._discrete_distns:nbinom_gen`

source: /scipy/stats/_discrete_distns.py :280

Signature

   class     nbinom_gen (    a    =  0   ,    b    =  inf   ,    name    =  None   ,    badvalue    =  None   ,    moment_tol    =  1e-08   ,    values    =  None   ,    inc    =  1   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A negative binomial discrete random variable.

Extended Summary

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Notes

Negative binomial distribution describes a sequence of i.i.d. Bernoulli trials, repeated until a predefined, non-random number of successes occurs.

The probability mass function of the number of failures for nbinom is:

f (k) = (n - 1 k + n - 1) p^{n} (1 - p)^{k}

for $k \geq 0$ , $0 < p \leq 1$

nbinom takes $n$ and $p$ as shape parameters where $n$ is the number of successes, $p$ is the probability of a single success, and $1 - p$ is the probability of a single failure.

Another common parameterization of the negative binomial distribution is in terms of the mean number of failures $μ$ to achieve $n$ successes. The mean $μ$ is related to the probability of success as

p = \frac{n}{n + μ}

The number of successes $n$ may also be specified in terms of a "dispersion", "heterogeneity", or "aggregation" parameter $α$ , which relates the mean $μ$ to the variance $σ^{2}$ , e.g. $σ^{2} = μ + α μ^{2}$ . Regardless of the convention used for $α$ ,

p n = \frac{μ}{σ ^{2}} = \frac{μ ^{2}}{σ ^{2} - μ}

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

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Aliases

scipy.stats._discrete_distns.nbinom_gen