For the binomial example (i.e. the case of extreme under-dispersion), we see that λ decreases and ν increases for m≤3.
For the negative binomial example, we see that the sCMP class of distributions again performs well in estimating the form of the simulated dataset.
In fact, the worst case for the binomial example using two moments (0.333) is already better than the best case for the truncated geometric using four moments (0.404).
However, the binomial example is more likely to survive.
Using four moments, the best case for the truncated geometric example (0.404, Table 2) is worse than the worst case for binomial example (0.207, Table 1).
For the binomial and the beta-binomial the logit link was used.
The hypergeometric is more comprehensive and precise than the binomial and the Poisson.
We obtain a general formula which encompasses, for example, the Poisson and binomial distributions, but concentrate on the negative binomial and gamma — partly replicating Zhu and Lakkis for the former [ 17] — because these can be used to model skewed data, for which normal approximations are less likely to be satisfactory.
For example, the binomial model allows the incorporation of changes in the risk posed by the underlying stock.
A few noteworthy examples are: Roebuck, French and Dennis (2004), who looked at the link between marijuana use, high school dropouts and truancy outcomes using as zero inflated negative binomial model; and Temple and Reynold (2007), who looked at the effectiveness of preschool participation on years of special education and on the number of arrests, using a zero inflated negative binomial model.
