Negative binomial and Poisson I am trying to see which model fits better to an email count data.Tried to fit the count data to Poisson using chi-square test. Did not fit.
Tried to fit the count data to Negative binomial by estimating the parameter, and using the chi-square test. Did not fit, although it reduced the chi-square statistic than that before.
What could be the error ? and how should i proceed ?
 A: Although the question is a bit vague, I will try to give some information. Frequency is more often modeled by:


*

*Poisson

*Negative Binomial

*Binomial


All these distributions are determined by their mean and variance. If 
$$\newcommand{\Var}{{\rm Var}}\frac{\Var[N]}{E[N]}\approx 1$$
you should choose Poisson where $E[N]=\Var[N]=\lambda$ .
If 
$$\frac{\Var[N]}{E[N]}>1$$
you should choose Negative Binomial where $E[N]=\alpha\beta$ and $\Var[N]=\alpha\beta(1+\beta)$.
If
$$\frac{\Var[N]}{E[N]}<1$$
you should choose Binomial where $E[N]=np$ and $\Var[N]=np(1-p)$.
The choice is not strictly mathematical. Parameters can be calculated by solving the equations. If you have enough data, you could calibrate parameters by calculating mean and variance for different periods. The Pearson chi-squared test is used for testing fitting performance but goodness of fit tests in general provide only indications and should not be your only criterion. Empirical vs theoretical distribution graphs could also help to determine fitting appropriateness.
You could also try to fit distributions with more parameters, like Conway-Maxwell-Poisson distribution but beware of over-fitting.
In case there are a lot of zeros you should see this article.
