The Pascal Distribution¶

gsl_ran_pascal(p, n)¶

This function returns a random integer from the Pascal distribution. The Pascal distribution is simply a negative binomial distribution with an integer value of n.

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

for \(k \geq 0\)

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

gsl_cdf_pascal_P(k, p, n)¶

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

The Negative Binomial Distribution

The Geometric Distribution