The Binomial Distribution¶

gsl_ran_binomial(p, n)¶

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

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

for \(0 \leq k \leq n\).

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

gsl_cdf_binomial_P(k, p, n)¶

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

The Bernoulli Distribution

The Negative Binomial Distribution