Premium
Extended Poisson Process Modelling and Analysis of Count Data
Author(s) -
Faddy M. J.
Publication year - 1997
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710390405
Subject(s) - poisson distribution , mathematics , compound poisson process , representation (politics) , count data , extension (predicate logic) , discrete poisson equation , variance (accounting) , compound poisson distribution , cox process , statistical physics , simple (philosophy) , process (computing) , distribution (mathematics) , poisson process , statistics , poisson regression , mathematical analysis , computer science , uniqueness theorem for poisson's equation , physics , population , philosophy , law , business , sociology , operating system , uniqueness , accounting , epistemology , political science , programming language , demography , politics
It is shown that any discrete distribution with non‐negative support has a representation in terms of an extended Poisson process (or pure birth process). A particular extension of the simple Poisson process is proposed: one that admits a variety of distributions; the equations for such processes may be readily solved numerically. An analytical approximation for the solution is given, leading to approximate mean‐variance relationships. The resulting distributions are then applied to analyses of some biological data‐sets.