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

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Poulomi Ganguli 2019-10-11

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回答： Abhishek Kumar 2020-12-8

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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John D'Errico 2019-10-11

编辑：John D'Errico 2019-10-11

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 2019-10-11

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

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Answer 1

Abhishek Kumar 2020-12-8

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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.