Abstract: In this paper, a multivariate version of the negative binomial-quasi Lindley (NB-QL) distribution is proposed, and some of the characteristics of the distribution are discussed. The bivariate NB-QL distribution is demonstrated as a special instance of the multivariate NB-QL distribution. This approach is suitable for use in any domain where overdispersion can be detected. The maximum likelihood estimation is used for estimating parameters through numerical optimization with R programming. A simulation to estimate parameters is illustrated. Furthermore, the empirical data detailing the frequency of faults occurring weekly in two feeders in Thailand are analyzed using univariate, bivariate, and conditional NB-QL distributions. The results indicate that the expected frequencies exhibit appropriate goodness of fit, suggesting that the proposed distribution can flexibly and appropriately model count data.

Keywords: Bivariate distribution, Bivariate negative binomial-Quasi Lindley, Multivariate distribution, Multivariate count data, Maximum likelihood estimation, Overdispersion

Pages: 756-765