Hi everyone, I need your help on my problem

If I want to find sum of n rician random variable, how I can do this? rice rv R~(m,s^2) , m is the rice mean and s^2 is the variance.

[Rik]

Do you have a way to describe it less compact? And can you describe how to generate your distribution from a normal distribution? Or is that impossible?

Answer 1

[Jeff Miller]

If n is more than a very small number, the sum of n of independent Ricians will be very close to normal with mean n*m and variance n*s^2 (central limit theorem), especially since the Rician is almost normal to begin with (for many parameter values, at least).

If n is too small to use the normal approximation, you will probably have to compute the distribution of the sum by numerical integration.

[Jeff Miller]

Here is the integral for n=2. For n=3 you need a double integral, and so on.

pd = makedist('Rician','s',0,'sigma',2);
x=0:.1:20;
xpdf = pd.pdf(x);
plot(x,xpdf);  % density of a single Rician
sum_pdf = zeros(size(x));
for i=1:numel(x)
    sum_pdf(i) = integral(@(s) pd.pdf(x(i)-s).*pd.pdf(s),0,x(i));
end
figure; plot(x,sum_pdf);  % density of the sum of 2 independent Ricians

[Jeff Miller]

Sorry, apparently I do not understand what you are trying to do (the attachments do not mean anything to me). Why did the code "not work well"?

[Jeff Miller]

I guess I don't know the answer you are looking for. Sorry I was not able to help.

[Walter Roberson]

Looks like the user deleted their contributions, which makes it difficult to figure out what was happening or how to solve their question.