Some gamma processes based on the dirichlet-gamma transformation
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 9 (1) , 123-143
- https://doi.org/10.1080/15326349308807257
Abstract
The purpose of this paper is to develop some extensions of the beta-gamma processes introduced by Lewis et al. (1989). We consider a univariate gamma ARMA(p,p-l) process and multiple gamma AR(1), MA(1) and ARMA(1,1) processes. These models are useful for modelling or generation of sequences of dependent (multiple) gamma random variables which arise in various fields. In developing each of these models we make use of the Dirichlet-gamma transformation. Several properties of the models such as autocorrelation, joint distribution, regression and time reversibility are investigated. The analogy between the gamma and the negative binomial distributions makes it possible to develop similar models for the negative binomial distribution.Keywords
This publication has 7 references indexed in Scilit:
- Continuous Multivariate DistributionsWiley Series in Probability and Statistics, 2000
- An integer-valuedpth-order autoregressive structure (INAR(p)) processJournal of Applied Probability, 1990
- First-order autoregressive models for gamma and exponential processesJournal of Applied Probability, 1990
- Gamma processesCommunications in Statistics. Stochastic Models, 1989
- Random Coefficient Autoregressive Models: An IntroductionPublished by Springer Nature ,1982
- First-order autoregressive gamma sequences and point processesAdvances in Applied Probability, 1980
- A new multivariate gamma distribution and its fitting to empirical streamflow dataWater Resources Research, 1978