modifying pdf of a GMM using gmdistribution

I have made a GMM using gmdistribution.fit on a dataset and now I'd like to alter the PDF by making the highs higher and the lows lower, for example by squaring or cubing the individual pdf values and then renormalizing so it sums to 1. The point is to emphasize the peaks of the distribution even more when sampling from the gmm. How can I transform the gmm in this way? Thanks!

Gene

[Eugene Kogan]

An alternative method would be constructing my own arbitrary pdf... how would you go about sampling from an arbitrary probability distribution. I prefer the first way as long as its possible to shape/modify the pdf somehow.

[Umar]

Hi Eugene,

First, load your dataset and fit a GMM using the fitgmdist function. Calculate the PDF values of the GMM using the pdf function.Apply a transformation to the PDF values (e.g., squaring or cubing) to emphasize peaks.Renormalize the transformed PDF values by dividing by the sum of the transformed values to ensure the distribution sums. Now, visualize the original and modified PDF on a plot to compare the effects of the transformation on the distribution. Hope this will help you resolve your problem now.

Answer 1

[Anshuman]

Hello,

To achive this, firstly evaluate the PDF of the GMM at a set of points. You can use the 'pdf' method available for a GMM object. Apply the transformation you desire, such as squaring or cubing the PDF values, to emphasize the peaks. After modifying the PDF values, you need to renormalize them so that they sum to 1. This involves dividing each modified value by the sum of all modified values. Now, use the modified PDF to sample from the distribution.

Hope it helps!