


The Logistic Distribution
=========================

.. function:: gsl_ran_logistic(a)

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

 .. math::
   p(x) dx = { \exp(-x/a) \over a (1 + \exp(-x/a))^2 } dx

 for :math:`-\infty < x < \infty`.

.. function:: gsl_ran_logistic_pdf(x, a)

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

.. function:: gsl_ran_logistic_P(x, a)

.. function:: gsl_ran_logistic_Q(x, a)

.. function:: gsl_ran_logistic_Pinv(P, a)

.. function:: gsl_ran_logistic_Qinv(Q, a)

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