BIVARIATE DISCRETE NADARAJAH AND HAGHIGHI DISTRIBUTION: PROPERTIES AND DIFFERENT METHODS OF ESTIMATION

Abstract

The exponential distribution is commonly used to model different phenomena in statistics and reliability engineering. A new extension of exponential distribution known as the Nadarajah and Haghighi [An extension of the exponential distribution, Statistics: A Journal of Theoretical and Applied Statistics, 2011,45, 543-558] was introduced in the literature to accommodate the inflation of zero in the data. However, in practice, discrete data is easy to collect as compared to continuous data. Thus focusing on the utility of discrete data, this study presents a new bivariate discrete Nadarajah and Haghighi distribution. We discuss several properties of the proposed distribution and study seven different methods of estimation to assess the performance of the proposed bivariate discrete model. Two data sets are analyzed to demonstrate how the proposed model may work in practice. By numerical finding, it is observed that the proposal is very flexible and produce superior results as compared to some existing models.