Some Results On Convolutions Of Heterogeneous Negative Binomial Random Variables

Convolutions of independent random variables often arise in a natural way in many applied areas including applied probability, reliability theory, life testing, actuarial science, and operations research.Since the distribution theory is quite complicated when the convolution involves independent and non-identical random variables,it is of great interest to investigate stochastic properties of convolutions. Many results have appeared in the literature, and most of them focus on exponential, gamma and geo-metric distributions. Negative binomial distribution is used commonly to model count data, especially in Bayesian inference. There are very few results on convolutions of heterogeneous negative binomial random variables due to the complexity of the dis-tribution theory. In this thesis, we apply the results on convolutions of heterogeneous gamma random variables to the situation of negative binomial random variables by a special relationship between their distributions.We study the likelihood ratio order, hazard rate order,mean residual life order between convolutions of two heterogeneous negative binomial sets of variables wherein they have differing parameters.The vari-ability between convolutions of two heterogeneous negative binomial sets of variables are also compared in terms of entropy.