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My question is almost identical to this one. I'm searching for a probability distribution for skewed data that allows for zeros. The purpose is to fit a GLM model. My data on species-area distributions are heavy right skewed. Additional variables are "partitioned area" according to latitude- so area in tropical and temperate zones, thus the data now includes zeros.

So my question is; is there a probability distribution, e.g. similar to the log-normal, but which allows for zeros?

Any pointers would be highly appreciated.

UPDATE

Histograms of my area data

enter image description here

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    $\begingroup$ The Gamma distribution is the canonical example, but perhaps you should post a histogram with your data so we can get more of a feel? Gamma regression isn't the most common GLM, but it may be very appropriate here. $\endgroup$ – user44764 Jun 13 '14 at 18:48
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    $\begingroup$ It's not clear, but you might be looking for zero-inflated models (which you can search about). $\endgroup$ – whuber Jun 13 '14 at 19:01
  • $\begingroup$ Unfortunately I said Gamma regression forgetting that $0$ is not in the support of the Gamma distribution. @whuber has the right of it $\endgroup$ – user44764 Jun 14 '14 at 1:54
  • $\begingroup$ I got suggested this paper on "The compound poisson-gamma model" which is appropriate for skewed, zero-inflated continuous data. onlinelibrary.wiley.com/doi/10.1111/2041-210X.12122/abstract $\endgroup$ – jO. Jun 16 '14 at 13:42
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The tweedie distribution is in the exponential family, hence can be used in a GLM context, and it allows for the occurrence of zeroes in the response variable. You could see if this suits your purpose.

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