Titre : Some Parametric Families of Single-Type Branching Distributions Auteurs : Rachid Senoussi, Ouaari Amel, Revue : Biostatistics and Health Sciences Numéro : Issue 1 Volume : 3 Date : 2022/09/5 DOI : 10.21494/ISTE.OP.2022.0865 ISSN : 2632-8291 Résumé : In this paper, we present some parametric families of probability distributions associated to particular single type homogeneous branching processes in continuous time. Their simplicity and the relevance of the interpretation of parameters for many domains of applications are of valuable interest for statistical inference. These families are particularly well adapted to handle branching dynamical systems of populations where Poisson assumption is generally but mistakenly assumed. Calculations and pertinent properties concerning these probability distributions are derived from their generating functions satisfying specific linear partial differential equations. As a by product, these equations allow the statement of a general recurrence formula for factorial moments. Éditeur : ISTE OpenScience