Matlab distribution fitting app

Question

I have a statistic and I want to determine its distribution, so before going through the simplification of the expression, I wanted to know what I'm looking for, so I used the distribution fitting app in Matlab. I found out that the "non parametric distribution" fitted perfectly, and I don't know what is meant by this distribution. Can you guys explain a bit what a non parametric distribution is?

Answer 1

There is no particular distribution known as "the non-parametric distribution". The adjective "non-parametric" describes a large class of distributions which have the characteristic that they are not defined by a small number of parameters. This class stands in contrast to the "parametric" distributions, all of which are completely characterized by a small number of parameters. The Normal, Beta, and Gamma distributions are all parametric, for example.

From the displayed chart, it seems that MatLab has merely smoothed the histogram somewhat, resulting in a typical example of a non-parametric distribution (in blue). It is characterized by all the bin heights of the individual bins of the histogram, about 55 or so.

Any empirically smoothed histogram qualifies as non-parametric. Whether it means anything to anybody is purely in the eyes of the beholder.

If the data is always less than or equal to zero, as it appears to be, then you might have much better luck fitting a four-parameter Beta distribution to your histogram. Specify as its endpoints zero and -180, and ask MatLab to estimate the remaining two parameters. The Wikipedia article on the "Beta distribution" has a lot of material on how to work with this nicely flexible distribution.