We develop two conditional tests for homogeneity of zero-inflated Poisson (ZIP) and Poisson-hurdle distributions. A Monte Carlo method is proposed for approximating the reference distributions of these tests. The techniques are applied to two examples.

Fiducial quantities are proposed to construct approximate tolerance limits and intervals for functions of some discrete random variables. Using established fiducial quantities for binomial proportions, Poisson rates, and negative binomial proportions, an approach is demonstrated to handle...

We prove large deviation principles for two versions of fractional Poisson processes: the main version is a renewal process, the alternative version is a weighted Poisson process. We also present asymptotic results for the ruin probabilities of an insurance model with a fractional Poisson claim...

Given a fixed time span for collecting observations in a study comparing, for example, the pathologies of patients entering a hospital sequentially, it is advisable to consider the sample sizes of the ANOVA levels as random variables. Using this approach, more powerful tests are developed,...

An original dataset referring to a medium-sized Italian university is implemented for analyzing the determinants of scientific research production at individual level. Three different indicators, based on the number of publications and/or citations, are considered. Their distributions are highly...

Purpose – The purpose of this paper is to use Bayesian probability theory to analyze the software reliability model with multiple types of faults. The probability that all faults are detected and corrected after a series of independent software tests and correction cycles is presented. This in...