How to integrate the Rice distribution and build a graph?

Hello. I need to integrate the Rice distribution to calculate the probability of optical signal error with mathematical expectation v=1, variance s=0.033. There should be a double integration of the Rice distribution, where the inner integral is from 0.9 to infinity, and the outer integral is from 0 to infinity.

Please help me write the working code for calculating and plotting. I've been trying to write for 3 weeks, nothing works, every time there's some kind of mistake, probably due to the fact that I have little experience on matlab.

[Torsten]

We are not familiar with the Rice distribution. How does the double integral with integrand look like in a mathematical notation ?

[Suleyman Aliyev]

[Suleyman Aliyev]

Oh, sorry, I forgot to add a graph for an example:

Answer 1

[Torsten]

As written, H is an integration variable - you cannot prescribe a value for it since it runs from 0 to Inf.

v = 1;
sigma = 0.033;
H = 0.9;
p = @(y)sqrt(y/v).*1/(sqrt(2*pi)*sigma).*exp(-(y-v).^2/(2*sigma^2));
I = integral2(@(H,x)p(x).*p(H),0,Inf,@(H)H,Inf)

I = 0.4999

[Suleyman Aliyev]

Thank you so much for your help!

Is it possible to plot the Rice distribution based on these values?

[Torsten]

v = 1;
sigma = 0.033;
p = @(y)sqrt(y/v).*1/(sqrt(2*pi)*sigma).*exp(-(y-v).^2/(2*sigma^2));
y = 0.9:0.001:1.1;
plot(y,p(y))

[Suleyman Aliyev]

Thank you very much, you helped me a lot!