Jumping at Zero Mass Point Convex Poisson Distribution and Its Fecundability Application

Abstract

In this article, a new Poisson type but convex discrete probability distribution is introduced, and it is named as Jumping at Zero Mass Point Convex Poisson (JZMPCP). When the usual Poisson distribution with its statistical properties are inappropriate in some scientific applications such as fecundability data analyses, the JZMPCP is an alternative possibility. In other words, JZMPCP could be tried in scenarios in which the data exhibit a Jump at Zero Mass Point and convexity with respect to a focal point. The JZMPCP yields the usual Poisson distribution as a case as a parametric marginality. Expressions of the properties for this novel JZMPCP distribution are derived and illustrated in the context of human fecundability data analyses.