A Class of Discrete Distributions of Orderk
- 1 December 2009
- journal article
- research article
- Published by Springer Nature in Journal of Statistical Theory and Practice
- Vol. 3 (4) , 795-803
Abstract
A generalized hypergeometric probability distribution of order k (GHPD(k)) is introduced as a generalization of several well-known discrete distributions of order k such as the cluster binomial, the cluster negative binomial and the extended Poisson distribution of order k. It is shown that all the moments of GHPD(k) exists finitely. Certain properties of the distribution are studied by deriving its probability mass function, recurrence relations for probabilities, raw moments and factorial moments. Certain mixtures of GHPD(k) is shown to be GHPD(k). Further GHPD(k) is obtained as a limit of another GHPD(k).Keywords
This publication has 14 references indexed in Scilit:
- A new class of discrete distributionsBrazilian Journal of Probability and Statistics, 2009
- Univariate Discrete Distributions2005
- Extended generalized Hypergeometric probability distributionsStatistics & Probability Letters, 2002
- Some Properties of the Stuttering Poisson DistributionCalcutta Statistical Association Bulletin, 1995
- Multivariate distributions of order κStatistics & Probability Letters, 1988
- On multiparameter distributions of order kAnnals of the Institute of Statistical Mathematics, 1988
- On generalized binomial and multinomial distributions and their relation to generalized Poisson distributionsAnnals of the Institute of Statistical Mathematics, 1986
- Discrete distributions of orderk on a binary sequenceAnnals of the Institute of Statistical Mathematics, 1985
- On discrete distributions of orderkAnnals of the Institute of Statistical Mathematics, 1984
- Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences1973