


The Lognormal Distribution
==========================

.. function:: gsl_ran_lognormal(zeta, sigma)

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

 .. math::
   p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} }
     \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx

 for :math:`x > 0`.

.. function:: gsl_ran_lognormal_pdf(x, zeta, sigma)

 This function computes the probability density :math:`p(x)` at :math:`x` for a
 lognormal distribution with parameters ``zeta`` and ``sigma``, using
 the formula given above.

.. function:: gsl_cdf_lognormal_P(x, zeta, sigma)

.. function:: gsl_cdf_lognormal_Q(x, zeta, sigma)

.. function:: gsl_cdf_lognormal_Pinv(P, zeta, sigma)

.. function:: gsl_cdf_lognormal_Qinv(Q, zeta, sigma)

 These functions compute the cumulative distribution functions
 :math:`P(x), Q(x)` and their inverses for the lognormal distribution
 with parameters ``zeta`` and ``sigma``.
