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.

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The Logistic Distribution

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The Weibull Distribution