# The Pareto Distribution¶

gsl_ran_pareto(a, b)

This function returns a random variate from the Pareto distribution of order a. The distribution function is,

$p(x) dx = (a/b) / (x/b)^{a+1} dx$

for $$x \geq b$$.

gsl_ran_pareto_pdf(x, a, b)

This function computes the probability density $$p(x)$$ at $$x$$ for a Pareto distribution with exponent a and scale b, using the formula given above.

gsl_cdf_pareto_P(x, a, b)
gsl_cdf_pareto_Q(x, a, b)
gsl_cdf_pareto_Pinv(P, a, b)
gsl_cdf_pareto_Qinv(Q, a, b)

These functions compute the cumulative distribution functions $$P(x), Q(x)$$ and their inverses for the Pareto distribution with exponent a and scale b.