Say I have a simulation that produces a single floating point number as a result, and a different number is produced each time the simulation runs. These numbers are randomly distributed according to some unknown distribution. I would like to approximate the underlying density distribution function based on a finite sample of numbers. I know that I could use a histogram, but the size of the bins, which is essentially arbitrary, will significantly affect the results. I would like a way to do this which has no arbitrariness.Any ideas?
Approximate a distribution function from a finite sample
numerics;statistics
Since a distribution function contains more information than the finite set of numbers you start with, you clearly have to add information in the process. This information comes in the form of a model that you assume, and whose parameters you adjust to make the model fit your finite sample. Unless the nature of your problem suggests some model, the choice will always be arbitrary to some extent.With a histgram, your model is that of a piecewise constant function with the pieces (bins) having a fixed width. With Kernel Density Estimation, your model is the kernel. There is no way around choosing a model, the best you can do is to make an informed choice based on what you know (or can reasonably assume) about your data.