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I have a data set with about 3000 members that I'd like to use as a feature for a binary classification algorithm. The variable seems to be skewed by nature because the histogram is tailed at pretty much any sample. Below is the current population:

enter image description here

So I have a few questions that hope those of you who are much more experienced might be able to help with.

  • Can I "fit" these data to a more suitable distribution than a normal one? Perhaps a chi square?
  • For a non-normal distribution, especially a tailed one like mine, is there something analogous to standard deviation that I can use to characterize a data point?

Thanks!

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  • $\begingroup$ Note: after posting, I realized I meant to add gamma as a potential fit $\endgroup$
    – R Vincent
    Dec 29, 2018 at 13:51
  • $\begingroup$ There are many relatively heavy-tailed, right-skewed distributions. Sometimes it is useful to identify the 'name' of such a distribution (in order to have a functional for for the PDF or CDF and to do inference), and sometimes not. // You might add Weibull, Rayleigh, and lognormal to your list of right-skewed distributions with support $(0, \infty).$ $\endgroup$
    – BruceET
    Dec 29, 2018 at 16:28
  • $\begingroup$ 1. Why would you need to identify a distribution if you're planing to use this as a feature? Aren't you just conditioning on it anyway? 2. It's unclear to me what you mean by "tailed at pretty much any sample"; you only appear to have one sample, and it's not clear to me what you intend by "tailed". $\endgroup$
    – Glen_b
    Dec 30, 2018 at 6:40

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FYI I was able to find a fitting algorithm with the following results:

enter image description here

Turns out that the best fit is "Inverse Gaussian"!

Now I need to gain an understanding of the parameters.

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