A COM-Poisson-type generalization of the negative binomial distribution |
| |
| Authors: | S Chakraborty S H Ong |
| |
| Institution: | 1. Department of Statistics, Dibrugarh University, Dibrugarh 786004, India;2. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysiasubrata_arya@yahoo.co.in;4. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia |
| |
| Abstract: | ABSTRACTThis paper introduces a generalization of the negative binomial (NB) distribution in analogy with the COM-Poisson distribution. Many well-known distributions are particular and limiting distributions. The proposed distribution belongs to the modified power series, generalized hypergeometric and exponential families, and also arises as weighted NB and COM-Poisson distributions. Probability and moment recurrence formulae, and probabilistic and reliability properties have been derived. With the flexibility to model under-, equi- and over-dispersion, and its various interesting properties, this NB generalization will be a useful model for count data. An application to empirical modeling is illustrated with a real data set. |
| |
| Keywords: | COM-Poisson Empirical modeling Equi- and over-dispersion Exponential families Generalized hypergeometric Increasing failure rate Index of dispersion Log-concavity Modified power series Reliability Stochastic ordering Under Unimodality Weighted distribution |
|
|
