I have a dataset in a CSV file which is a single column of positive integers. I would like to know which probability distribution it fits.

The histogram is as follows.

enter image description here

This is how I am trying.

w = Transpose[Import["dataset.csv"]][[1]];
h = DistributionFitTest[w, SkewNormalDistribution[12, 7, 0.1], "HypothesisTestData"];
Show[Histogram[w, Automatic, "ProbabilityDensity"], 
 Plot[PDF[h["FittedDistribution"], x], {x, 0, 80}, 
  PlotStyle -> Thick]]

The output is:

enter image description here

Can I claim that my dataset has a skewed normal distribution?


1 Answer 1


This is an extended comment to echo @MarcoB 's comment that this question would be better served on Cross Validated.

Your data consists of only even integers that range from 0 to 72. While you can probably find a discrete probability distribution that will produce similar observed histograms (like maybe twice a negative binomial), the repeatable patterns in the sequence of observations negates being able to talk about your data as if it was a random sample from such a distribution.

Here is a plot of the observations in sequence:

Data in sequence

Consideration of how the data is generated can be even more important that just providing a compact summary/approximation of the observed histogram.

  • $\begingroup$ @Jim, what is the systematic way to find distribution in these scenarios? $\endgroup$ May 9, 2016 at 21:37
  • $\begingroup$ @JimB Yeah, well, isn't that a fact...(+1). $\endgroup$
    – Carl
    Aug 5, 2022 at 16:20

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