The Logistic Distribution¶

gsl_ran_logistic(a)¶

This function returns a random variate from the logistic distribution. The distribution is,

\[p(x) dx = { \exp(-x/a) \over a (1 + \exp(-x/a))^2 } dx\]

for \(-\infty < x < \infty\).

gsl_ran_logistic_pdf(x, a)¶: This function computes the probability density \(p(x)\) at \(x\) for a logistic distribution with scale parameter a, using the formula given above.

gsl_ran_logistic_P(x, a)¶

gsl_ran_logistic_Q(x, a)¶

gsl_ran_logistic_Pinv(P, a)¶

gsl_ran_logistic_Qinv(Q, a)¶: These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the logistic distribution with scale parameter a.

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The Beta Distribution

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The Pareto Distribution