How Do You Fit a Distribution to Truncated Data for Extrapolation?

[lagfish]

Hi Math Experts,
I have a two part question:
Let's say I have a set of data and I want to fit a distribution to it, but I have to get rid of all the data below some threshold value, so that a large part of the left side of the histogram is cut off. How would I go about fitting a distribution to this data so that I can extrapolate for the missing parts? I have access to Matlab and whatever trial software is free.

Let's say that the data is from an experiment for some physical process, for which I don't know which distribution function best models it. Do I just pick the one with the best fit? Or is there some sort of standard function that mathematicians use?

Thanks!

 

[Rajini]

Hi,
If you know the theory (math) of the physical process you can fit your data.
For example many spectroscopic data are usually fitted using Lorentzian or Gaussian or Voigt functions. Do you want to fit some part of your experimental data ? Then you can use gnuplot by fixing the fit range for x-axis, i mean the part of the x-data you are interested in. What is your data/experiment you want to fit.

 

[lagfish]

Thanks for the reply.
I'm not sure if what you're describing is what I want to do, so I've attached a picture:

Let's say I have to remove the information on all the white portions, and I want to end up with a distribution function close to the purple - is this possible?

The experiment I want to fit is there is a cylindrical container with two balls inside that I am shaking in a regular repeated pattern. The data is all of the normal velocities of the balls when they hit one end of the container. I've looked up a few functions and couldn't find any that would model this process.