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I am struggling to find an appropriate distribution to model the total number of vacation days taken in a year.

I originally thought of going with a standard count distribution like negative binomial or even using hurdle regression to combine negbin with a logistic model. However, the nature of the dependent variable makes me second guess my choices.

The problem I have is that I am trying to predict the total number of days and these are not independent events. If I was modeling "# of vacations" and not days, I would be more willing to use a count model. I have searched all over for things like "duration modeling" but I am not finding anything helpful.

Any suggestions to point me in the right direction are greatly appreciated.

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    $\begingroup$ Depending on the available explanatory variables, you might think of using Poisson regression. $\endgroup$ – user10525 May 15 '12 at 22:24
  • $\begingroup$ Fitting a model to the frequency of the event, and then combinging that with a second model for the scale/duration/magnitude of that event, is a common problem for actuaries. Eg a negbin model for number of accidents, and some gamma or similar for how much they cost. Could be one way to go. $\endgroup$ – Peter Ellis May 16 '12 at 2:34
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I don't know what is out there in the literature but since you said that you would be willing to use a count model to predict the number of vacations why not do that and set it up in a hierarchical fashion that involves fitting a distribution for the number of days per vacation. Then take number of vacations and based on a likelihood approach take the highest mode of the number of vacation days, take the number of days for the mode and multiple it by the count model estimate for vacation days. If there is a tie for the mode maybe an arbitrary pick would be reasonable. Just a thought.

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