Generalized Pareto Distribution （GPD）

广义帕雷托分布

广义Pareto分布

 

MATLAB中如何产生pareto分布

函数   X = gprnd(X,K,sigma,theta,[M,N,...])  。当 sigma=theta 时，就可以生成通常的pareto分布。
X = gprnd(1/2,15,15,1,10^6)，即尾部参数为 alpha=2, 位置参数为 k = 15。

function r = gprnd(k,sigma,theta,varargin)
%GPRND Random arrays from the generalized Pareto distribution.
%   R = GPRND(K,SIGMA,THETA) returns an array of random numbers chosen from the
%   generalized Pareto (GP) distribution with tail index (shape) parameter K,
%   scale parameter SIGMA, and threshold (location) parameter THETA.  The size
%   of R is the common size of K, SIGMA, and THETA if all are arrays.  If any
%   parameter is a scalar, the size of R is the size of the other parameters.
%
%   R = GPRND(K,SIGMA,THETA,M,N,...) or R = GPRND(K,SIGMA,[M,N,...]) returns
%   an M-by-N-by-... array.
%
%   When K = 0 and THETA = 0, the GP is equivalent to the exponential
%   distribution.  When K > 0 and THETA = SIGMA, the GP is equivalent to the
%   Pareto distribution. The mean of the GP is not finite when K >= 1, and the
%   variance is not finite when K >= 1/2.  When K >= 0, the GP has positive
%   density for X>THETA, or, when K < 0, for 0 <= (X-THETA)/SIGMA <= -1/K.
%
%   See also GPCDF, GPFIT, GPINV, GPLIKE, GPPDF, GPSTAT, RANDOM.
%   GPRND uses the inversion method.
%   References:
%      [1] Embrechts, P., C. Klüppelberg, and T. Mikosch (1997) Modelling
%          Extremal Events for Insurance and Finance, Springer.
%      [2] Kotz, S. and S. Nadarajah (2001) Extreme Value Distributions:
%          Theory and Applications, World Scientific Publishing Company.
%   Copyright 1993-2005 The MathWorks, Inc.
%   $Revision: 1.1.6.1 $  $Date: 2005/05/31 16:44:41 $