On a Distribution Associated with a Stochastic Process in Ecology

✍ Scribed by K.G. Janardan

• Publisher: John Wiley and Sons
• Year: 2002
• Tongue: English
• Weight: 258 KB
• Volume: 44
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/1521-4036(200206)44:4<510::aid-bimj510>3.0.co;2-k

✦ Synopsis

Poisson processes fXðtÞ; t ! 0g 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 ½i.e. VðXðtÞÞ > EðXðtÞÞ or under-dispersion ½i.e. VðXðtÞÞ < EðXðtÞÞ is encountered. This led Consul and Jain (1973), andJanardan andSchaeffer (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.