There might be some nuances in the numerical integration, but here is the basic idea. You need to approximate the integral of x over the pdf.
% For reproducibility
rng default
% Simulated data -- normal centered on x=5.
N = 1000000;
x = 5 + randn(N,1);
% Get the probability density function. (You have these values already?)
[pdf_x,xi] = ksdensity(x);
% The bin width. (In this case, they are all equal, so I just take the first one.)
dx = xi(2) - xi(1);
% Calculate the total probability. (It should be 1.)
total_probability = sum(pdf_x*dx)
% Calculate the mean, which is the expected value of x.
mean_x = sum(xi.*pdf_x*dx)
2 Comments
Direct link to this comment
https://ww2.mathworks.cn/matlabcentral/answers/486796-how-can-i-effectively-compute-expected-value-by-histogram-approximation-of-probability-desnsity-func#comment_759063
Direct link to this comment
https://ww2.mathworks.cn/matlabcentral/answers/486796-how-can-i-effectively-compute-expected-value-by-histogram-approximation-of-probability-desnsity-func#comment_759063
Direct link to this comment
https://ww2.mathworks.cn/matlabcentral/answers/486796-how-can-i-effectively-compute-expected-value-by-histogram-approximation-of-probability-desnsity-func#comment_759068
Direct link to this comment
https://ww2.mathworks.cn/matlabcentral/answers/486796-how-can-i-effectively-compute-expected-value-by-histogram-approximation-of-probability-desnsity-func#comment_759068
Sign in to comment.