simulation of a probability on Matlab

Hi everyone,

I have this density of proability

p(x1,x2,x3,x4)=log2(1+x1/(1+(x2+x3+x4)))*x1*x2*x3*x4/sigma*exp(-(x1^2+x2^2+x3^2+x4^2)/sigma)

and I want to simulate the multiple integral of p(x1,x2,x3,x4)dx1 dx2 dx3 dx4

Is it possible on Matlab, if yes how can I do it?

Thank you so much for your help

Answer 1

[Parag]

Hi,

I understand that you want to use density function p(x1,x2,x3,x4)=log2(1+x1/(1+(x2+x3+x4)))*x1*x2*x3*x4/sigma*exp(-(x1^2+x2^2+x3^2+x4^2)/sigma) and simulate the multiple integral .

Yes, it is possible in MATLAB to simulate the multiple integral. Please find the below MATLAB code.

sigma = 1; 
pdf = @(x1, x2, x3, x4) log2(1 + x1 ./ (1 + (x2 + x3 + x4))) .* x1 .* x2 .* x3 .* x4 ./ sigma .* ...
    exp(-(x1.^2 + x2.^2 + x3.^2 + x4.^2) / sigma);

num_samples = 1e6;

lower_limit = -10;
upper_limit = 10;

x1_samples = lower_limit + (upper_limit - lower_limit) * rand(num_samples, 1);
x2_samples = lower_limit + (upper_limit - lower_limit) * rand(num_samples, 1);
x3_samples = lower_limit + (upper_limit - lower_limit) * rand(num_samples, 1);
x4_samples = lower_limit + (upper_limit - lower_limit) * rand(num_samples, 1);

f_values = pdf(x1_samples, x2_samples, x3_samples, x4_samples);

volume = (upper_limit - lower_limit)^4;

integral_estimate = volume * mean(f_values);

disp(['Estimated integral: ', num2str(integral_estimate)]);

Estimated integral: -0.16002+0.046327i

To know more about multiple integral check this

https://www.mathworks.com/help/matlab/ref/integral2.html