Count models are a subset of discrete response regression models. Count data are distributed as non-negative integers, are intrinsically heteroskedastic, right skewed, and have a variance that increases with the mean. Example count data include such situations as length of hospital stay, the number of a certain species of fish per defined area in the ocean, the number of lights displayed by fir...

We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employ...

Various authors [3, 9, 11, 12] have noted that Poisson regression can be used to analyze cohort survival data (see Cohort Study). This formulation also leads to a unification of risk estimation based on internal comparison of rates among members of a cohort with various exposure levels and classical epidemiologic methods based on external rates that yield standardized mortality ratios or standa...

Critics of voting by mail express concern over its impact on civil society. For example, Thompson (2004) posits that voting by mail limits electoral civic engagement by preventing the temporal norm of simultaneity on Election Day. I, however, find that the open ballot system of voting by mail promotes deliberation, which encourages civic engagement. This study tests if voting by mail increases ...

In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums. The PF2 property reveals the monotonicity property of the reversed failure rates of certain compound...

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable W satisfies a certain negative dependence assumption, then W is smaller (in the convex sense) than a Poisson variable of equal mean. Such W include those which may be written as a sum of totally negatively dependent indicators. This is generalised to other stochastic orderings. Application...