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On a Distribution Associated with a Stochastic Process in Ecology
Author(s) -
Janardan K.G.
Publication year - 2002
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 - 10.1002/1521-4036(200206)44:4<510::aid-bimj510>3.0.co;2-k
Subject(s) - poisson distribution , mathematics , distribution (mathematics) , population , generalization , stochastic modelling , statistical physics , dispersion (optics) , statistics , compound poisson distribution , ecology , physics , mathematical analysis , poisson regression , biology , sociology , demography , quantum mechanics
Poisson processes { X ( t ), t ≥ 0} are suitable models for a broad variety of counting processes in Ecology. For example, when analyzing data that apparently came from Poisson population, over‐dispersion [i.e. V ( X ( t )) > E ( X ( t ))] or under‐dispersion [i.e. V ( X ( t )) < E ( X ( t ))] is encountered. This led Consul and Jain (1973), and Janardan and Schaeffer (1977) to consider a generalization of the Poisson distribution called Lagrangian Poisson distribution. Janardan (1980) modified the Poisson process and derived a stochastic model for the number of eggs laid by a parasite on a host. This distribution is very suitable for fitting data with over‐ (or under‐) dispersion. Janardan et al. (1981) considered this stochastic model and applied it to study the variation of the distribution of chromosome aberrations in human and animal cells subject to radiation or chemical insults. Here, we present a new approach for the derivation of this distribution and provide some alternative chance mechanisms for the genesis of the distribution. Moments, moment properties, and some applications are also given.