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Match data by using a weighted sum of 4-parameter beta distribution?

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Dear All,

I wrote a code in Mathematica, which tries to match the data by using a weighted sum of 4-parameter beta distribution. I have real-world frequency data, that look like quite comlex. As you will see, I manually sketched some “sub-distributions”, total 7 in general. I thought using a highly flexible 4-parameter beta distribution is a way to go. However, my FindFit command gives an error message, and you can see from the plot the fit is far from perfect. I suppose the problem arises due to the poor guess values, but I have no clue how to rectify the issue.

Can somebody please help? Please note I must have analytic expression in the end, that is why I used a weighted sum of known densities. The mathematica code as well as the manually sketched images are attached.

POSTED BY: Alex Token
Answer
2 months ago

Have you considered of using the function

EstimatedDistribution

? yehuda

POSTED BY: Yehuda Ben-Shimol
Answer
2 months ago

Dear Yehuda, thank you for your reply. My issue is I am not fitting raw data to a distribution, I have an empirical PDF of that distribution. I suppose that won't work as "EstimatedDistribution" works with the raw measurement data, not frequencies.

POSTED BY: Alex Token
Answer
2 months ago

data has 33 points Your model requires values for 35 parameters (5 parameters x 7 components). I find it hard to believe that you will find a solution where you have more unknown parameters that data Again, I recommend on using the function EstimatedDistribution, on the real data, since I assume you have much more points there. In addition, to define a distribution as a mixture of several distributions, you need to look at MixtureDistribution HTH yehuda

POSTED BY: Yehuda Ben-Shimol
Answer
2 months ago

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