Number of events estimation

I have three different histograms (Impact parameter distributions) corresponding to three groups of the same particle with different properties. However, the three distribution have more or less the same shape. Now I want to predict a fourth distribution (with another property), which should have more or less the same shape as the three other ones. I have only a part of this latter distribution in a certain range.

A first attempt was to predict the rest of the distribution using a Transfer Factor (TF), which is the ratio of integrals in two different ranges, and by multiplying this TF to the integral of the known range in the fourth distribution, I could estimate the number of events in the unknown range. I did this using the three known distribution, but I obtained three different results, which were not even close to each other. I think that one of the three must be the good one, but I don't know which one.

My question: Is there a statistical method to determine the best one? or is there another way/method to approximate my last distribution?

Topic distribution parameter-estimation statistics

Category Data Science

1
answered at

It appears that you can the problem with polynomial regression. There is a single target "entries" and two features: 1: numeric "d0" and 2: categorical "Mu" type. Then try different polynomial orders to closely match the distributional shape.

After training the model, you'll predict the new data.

There are many ways to evaluate a model. The two common are:

  1. Goodness of fit - How well does the model fit the training data?

  2. Predictive - How well does the model predict novel data?

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