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.
Have you considered of using the function
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.
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