


The Beta Distribution
=====================

.. function:: gsl_ran_beta(a, b)

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

 .. math::
   p(x) dx = {\Gamma(a+b) \over \Gamma(a) \Gamma(b)}
     x^{a-1} (1-x)^{b-1} dx

 for :math:`0 \leq x \leq 1`.

.. function:: gsl_ran_beta_pdf(x, a, b)

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

.. function:: gsl_cdf_beta_P(x, a, b)

.. function:: gsl_cdf_beta_Q(x, a, b)

.. function:: gsl_cdf_beta_Pinv(P, a, b)

.. function:: gsl_cdf_beta_Qinv(Q, a, b)

 These functions compute the cumulative distribution functions
 :math:`P(x), Q(x)` and their inverses for the beta distribution with
 parameters ``a`` and ``b``.
