In this note we clarify the relationship between the local and global definitions of dual pairs in Poisson geometry. It turns out that these are not equivalent. For the passage from local to global one needs a connected fiber hypothesis (this is well known), while the converse requires a dimension condition (which appears not to be known). We also provide examples illustrating the necessity of ...

Count data often exhibit overdispersion and/or require an adjustment for zero outcomes with respect to a Poisson model. Zero-modified Poisson (ZMP) and zeromodified generalized Poisson (ZMGP) regression models are useful classes of models for such data. In the literature so far only score tests are used for testing the necessity of this adjustment. For this testing problem we show how poor the ...

Abstract Many researchers have shown interest in profile monitoring; however, most of the applications this field research are developed under assumption normal response variable. Little attention has been given to monitoring with non-normal variables, known as general linear models which consists two main categories (i.e., logistic and Poisson profiles). This paper aims monitor problem Phase I...

At the point when there is collinearity between reaction variable and various illustrative factors, displaying connection a few informative factors troublesome. While surveying count information, Poisson relapse model (PRM) generally utilized in applied research. A shrinkage assessor consistently answer for multicollinearity issue. One of these assessors Kibria Lukman (K-L). In this paper, jack...

The main purpose of this article is to present a new class bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting the positive correlation between number claims from third-party liability bodily injury property damage. Maximum likelihood estimation family achieved through an expectation-maximization al...