How to implement MonteCarlo integration of probability density function to obtain CDF

Hello:

I have a probability density function obtained from convolution process of two random variables. Hence, I don't have the functional form of the PDF. Now, I am interested to integrate the PDF numerically using Montecarlo method. I came across a few file exchage page, for example: https://de.mathworks.com/matlabcentral/fileexchange/53477-monte-carlo-integration

But above require functional form. Any suggestions/help how do I integrate the PDF using Montecarlo method to get corresponding CDF?

[Jeff Miller]

By convolution, you mean the sum of the two random variables, right?

Do you have the functional forms of the PDFs or CDFs for each of the two separate random variables?

Would you be happy with the convolution PDF/CDF obtained by some other numerical means, or does it have to be specifically with the Monte Carlo method?

[Poulomi Ganguli]

I have tried with trapz method but I want to check the result using Monte Carlo method since using trapz the obtained CDF series sometimes less than 1.

[John D'Errico]

Note that trapezoidal rule integration is not an EXACT integral. It is an approximation. The magnitude of the error will be impacted by the increment, generally larger for larger increments. So why are you surprised at the result?

[Poulomi Ganguli]

So, I want MonteCarlo method to get better CDF estimate.

Answer 1

[Abhishek Kumar]

Hi Poulomi, as I understand you have PDF of your desired function as convolution of two random functions(assuming f1,f2), you also have the file exchange script as you have mentioned hence you can use the following strategy.

(desired PDF as pdf)

pdf = conv(f1,f2);

[cdf,E,R,info]=integralN_mc(pdf);

"integralN_mc" being the function created under the script, you can use other variations of the functions as described in the script as well.

Please do share what input random functions you are using for further help if your query is not resolved.