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

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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?

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Poulomi Ganguli
Poulomi Ganguli on 11 Oct 2019
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
John D'Errico on 11 Oct 2019
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?

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Accepted Answer

Abhishek Kumar
Abhishek Kumar on 8 Dec 2020
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.

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