stblest.m

matlab alpha稳定分布

% Alpha稳定分布参数估计
function [alpha_est gama_est]=stblest(U)
% U：待估计数据
% 1------Parameter Estimation of Positive Alpha-Stable Distribution------
% 参考："Parameter Estimation of Positive Alpha-Stable Distribution Based on Negative-Order Moments"
% % 式（8），（9）
% Ce=0.57721566;
% V=log(abs(U));
% alpha_est=sqrt(pi^2/(6*var(V)+pi^2));
% log_gama=alpha_est*(mean(V)-Ce*(1/alpha_est-1)-log(sec(pi*alpha_est/2)^2)/(2*alpha_est));
% gama_est=exp(log_gama);

% 2------实对称Alpha稳定分布（SαS）参数估计------
% 参考："Parameter estimation and blind channel identification in impulsive signal environments"
% 式（17），（18）
% Ce=0.57721566;
% V=log(abs(U));
% alpha_est=sqrt(1/(6*var(V)/(pi^2)-0.5));
% log_gama=alpha_est*(mean(V)-Ce*(1/alpha_est-1));
% gama_est=exp(log_gama);

% 3------isotropic complex  SαS参数估计------
% 参考："Parameter estimation and blind channel identification in impulsive signal environments"
% 式（22），（23）
Ce=0.57721566;
V=log(abs(U));
alpha_est=sqrt(pi^2/(6*var(V)));
log_gama=alpha_est*(mean(V)-Ce*(1/alpha_est-1)-log(2));
gama_est=exp(log_gama);