I have the energy specter acquired from experimental data. After normalization, it can be used as a probability density function(PDF). I can construct a Cumulative distribution function(CDF) on a given interval using its definition as the integral of PDF. This integral simplified as a sum because of the PDF given in discrete form. I want to generate random numbers from this CDF.
I used Inverse transform sampling replacing CDF integral with sum. From then I am following the standard routine of the Inverse transform sampling solving it for sum range instead of an integral range.
My sampling visually fits experimental data but I wonder if this procedure is mathematically correct and how it could be proofed?
It can be used, just recommend that you analyze all the variables
Inverse transform sampling can be applied to both continuous and discrete probability distributions. The algorithm for the discrete version of the inverse transform is slightly different. You can refer to the following links.
https://stephens999.github.io/fiveMinuteStats/inverse_transform_sampling.html https://www.sciencedirect.com/topics/computer-science/inverse-transform
The ideas are ok but you need to do things that show your summs converge to the integral. Referring to a text on harmonic analysis or numerical analysis would probably be beneficial.
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