Statistical inference for distributions with one Poisson conditional.

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals. However, it is known, from research on conditionally specified models, that Poisson marginals will be encountered, together with both conditionals being of the Poisson form, only in the case in which the variables are independent. In order to have a flexible dependent bivariate model with some Poisson components, in the present article, we will be focusing on bivariate distributions with one marginal and the other family of conditionals being of the Poisson form. Such distributions are called Pseudo-Poisson distributions. We discuss distributional features of such models, explore inferential aspects and include an example of applications of the Pseudo-Poisson model to sets of over-dispersed data.

On bivariate pseudo-exponential distributions.

A bivariate conditionally specified distribution is one in which the dependence relationship between the two random variables is accomplished by defining the distribution of one of the random variables, given the other. One such conditionally specified model is called the pseudo-exponential distribution, where both the marginal distribution of one and the conditional distribution of the other, given the first, are exponential. In this paper, a variation of this conditioning regime is introduced, and its characteristics are contrasted with the original. An example is used to demonstrate the applicability of the new model. Per-capita Gross Domestic Product (GDP) is a measure of a nation's total annual production of goods and services, divided by its population. Two variations of both the original and the new conditioning regime are applied to GDP and infant mortality data across nations and territories. Possible generalizations are considered.

A simple approach for monitoring business service time variation.

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much of the data in service industries comes from processes having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this paper, we propose a new asymmetric EWMA variance chart (EWMA-AV chart) and an asymmetric EWMA mean chart (EWMA-AM chart) based on two simple statistics to monitor process variance and mean shifts simultaneously. Further, we explore the sampling properties of the new monitoring statistics and calculate the average run lengths when using both the EWMA-AV chart and the EWMA-AM chart. The performance of the EWMA-AV and EWMA-AM charts and that of some existing variance and mean charts are compared. A numerical example involving nonnormal service times from the service system of a bank branch in Taiwan is used to illustrate the applications of the EWMA-AV and EWMA-AM charts and to compare them with the existing variance (or standard deviation) and mean charts. The proposed EWMA-AV chart and EWMA-AM charts show superior detection performance compared to the existing variance and mean charts. The EWMA-AV chart and EWMA-AM chart are thus recommended.