how to model this type of distribution? I am trying to model this distribution in a generalized mixed model. the variable is a measure of number of number of years, reflecting start to end of reproduction, i.e. reproductive period. This variable shows zero inflation followed by a slightly skewed distribution. How can I model this type of distribution, I thought about a zero inflated Poisson but is number of years considered a count? it is true that I only have integer values for this variable since I subtract two ages, but since it is number of years I did not consider it as count data. Would appreciate the help.
here are the plots of the variable.


 A: Number of years is not really a count, but a duration. I would not expect it to follow the mean-variance relationship in the Poisson -- but you can't tell from the histogram in any case because you're looking at the marginal distribution of the response not the conditional distribution. (i.e. if you plot the response variable itself, you're not really looking at anything about which an assumption is required; this issue also applies to GLMs and even to multiple regression, where people - and quite a few textbooks - often make the same mistake. I've even seen one text that correctly explains this problem, and then proceeds to fall into exactly the error it warned against, and does so repeatedly.)
Even though reproductive period is recorded in years, I'd be inclined to use a zero-inflated continuous model (say a gamma). If you must use a discrete model, perhaps a zero-inflated negative binomial or a zero-inflated quasi-Poisson might be adequate. Failing that a mixture model might work reasonably well, though the need for something like that would depend in part on what your purposes are.
