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

GROUPS:
 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. Attachments:
 Have you considered of using the function EstimatedDistribution ? yehuda