廣義帕雷託分佈
廣義Pareto分佈
MATLAB中如何產生pareto分佈
函式 X = gprnd(X,K,sigma,theta,[M,N,...]) 。當 sigma=theta 時，就可以生成通常的pareto分佈。
X = gprnd(1/2,15,15,1,10^6)，即尾部引數為 alpha=2, 位置引數為 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 $