function f = kernel(xa,x,h);%KERNEL:  Density (1D) estimation using a Gaussian Kernel%         Density Estimator. This is  used to compute the plugin %         estimators of entropy%% Silverman, B. W. (1986). Density Estimation for % Statistics and Data Analysis. Chapman and Hall: London%%  IN   xa:       density axis f=f(xa)   %       x:        deviates %       h:        Kernel width%%  OUT  f:        Gaussian Kernel Density Estimator%%  Recommended h,  h = 1.06 * nx^-0.2 * sigma%  but not sure if this is a good value.%%  Example:%           x = randn(100,1); %           xa = [-5:0.1:5]; %           nx = length(x);%           h = 1.06 * (nx^-0.2) * std(x);%           f = kernel(xa,x,h);%           plot(xa,f);%%%  Author(s): M.D.Sacchi (sacchi@phys.ualberta.ca)%  Copyright 1988-2005 SeismicLab%  Revision: 1.2  Date: Ago/2005%%  Signal Analysis and Imaging Group (SAIG)%  Department of Physics, UofA% nxa = length(xa); f = zeros(nxa,1); nx = length(x); c = 1/sqrt(2*pi); [X,Xa] = meshgrid(x,xa); arg = (X-Xa)/h; f = exp(-0.5*arg.^2); f = sum(f,2); f = c*f'/nx/h;