The Negative Binomial Distribution¶

gsl_ran_negative_binomial(p, n)¶

This function returns a random integer from the negative binomial distribution, the number of failures occurring before n successes in independent trials with probability p of success. The probability distribution for negative binomial variates is,

\[p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k\]

Note that n is not required to be an integer.

gsl_ran_negative_binomial_pdf(k, p, n)¶: This function computes the probability \(p(k)\) of obtaining \(k\) from a negative binomial distribution with parameters p and n, using the formula given above.

gsl_cdf_negative_binomial_P(k, p, n)¶

gsl_cdf_negative_binomial_Q(k, p, n)¶: These functions compute the cumulative distribution functions \(P(k), Q(k)\) for the negative binomial distribution with parameters p and n.

The Binomial Distribution

The Pascal Distribution