# 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.