cdfGenPareto ============================================== Purpose ---------------- Computes the cumulative distribution function for the Generalized Pareto distribution. Format ---------------- .. function:: p = cdfGenPareto(x, loc, scale, shape) :param x: Values at which to evaluate the Generalized Pareto cdf. :math:x > 0. :type x: NxK matrix, Nx1 vector or scalar :param loc: Location parameter, ExE conformable with *x*. :type loc: NxK matrix, Nx1 vector or scalar :param scale: Scale parameter, ExE conformable with *x*. :math:scale > 0. :type scale: NxK matrix, Nx1 vector or scalar :param shape: Shape parameter, ExE conformable with *x*. :type shape: NxK matrix, Nx1 vector or scalar :return p: Each element in *p* isthe Generalized Pareto cdf evaluated at the corresponding element in *x*. :rtype p: NxK matrix, Nx1 vector or scalar Examples --------- :: // Set location parameter loc = 0; // Set scale parameter scale = 2; // Set shape parameter shape = 5; p = cdfGenPareto(3, loc, scale, shape); After the above code, p is equal to :: 0.3482 Remarks ------- The cumulative distribution function for the Generalized Pareto distribution is defined as: .. math:: f(x,\mu,\sigma,k) = \begin{cases} 1 - (1 + k\frac{x-\mu}{\sigma})^{\frac{-1}{k}},& k \ne 0\\ 1 - exp(-\frac{x-\mu}{\sigma}), & k = 0 \end{cases} .. seealso:: :func:pdfGenPareto