My data shows this distribution:

enter image description here

I am looking for a statistical distribution which my data follows. Thought about poisson distribution, but goodness of fit test shows p < 0.05

  • 1
    $\begingroup$ The peak on the left, is that censored data? Is it out of range data? Is it data below detection limit replaced with a value? Is it true 0 data? Many other possibilities exist, what it is determined how you handle it. $\endgroup$
    – ReneBt
    Feb 8, 2019 at 8:06
  • $\begingroup$ The 0 data are real values which were measured. In reality, the 0 data represent areas on which "no" human influence has been measured. Accordingly the value of 100000 represents a very high human influence on the respective area. $\endgroup$
    – Fab
    Feb 8, 2019 at 8:14
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    $\begingroup$ Don't apply log to variables with meaningful zeros. You can try sqrt (if you don't have negative values) or power transforms instead if the data is very skewed. But as probably the input is integer, I'd prefer a model that doesn't need this. $\endgroup$ Feb 8, 2019 at 10:11
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    $\begingroup$ Distributions do not, and never can, determine methods of statistical analysis. At the very least, you need to tell us what you intend to do with your distributional fit. What's it for, exactly? $\endgroup$
    – whuber
    Feb 8, 2019 at 13:01
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    $\begingroup$ Since you describe only a univariate distribution, it has little or no bearing on the question of relationships with other data. $\endgroup$
    – whuber
    Feb 13, 2019 at 13:05

1 Answer 1


It is not really two peaks, but it is just that the value 0 is special. This is also indicated by the fact that you are using a logarithmic plot, in which the value 0 does not quite fit. I think it makes most sense to treat the value 0 specially in the analysis. One, estimate the probability of 0. Two, estimate the conditional distribution of your observation given that it is nonzero. Formally, this is a mixture model: a mixture of a point mass at 0 and a probability density. In general, inference of mixture models is complicated, but here it is easy, because one of the components (the point mass) is fixed.

Edit: The technical term for this phenomenon is "zero inflation."


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