Abstract In this paper, we introduce a new distribution on Z, which can be viewed as a natural bivariate extension of the Skellam distribution. The main feature of this distribution a possible dependence of the univariate components, both following univariate Skellam distributions. We explore various properties of the distribution and investigate the estimation of the unknown parameters via the...

This paper uses computer simulations to verify several features of the Greatest Deviation (GD) nonparametric correlation coefficient. First, its asymptotic distribution is used in a simple linear regression setting where both variables are bivariate. Second, the distribution free property of GD is demonstrated using both the bivariate normal and bivariate Cauchy distributions. Third, the robust...

The Gompertz distribution has many applications, particularly in medical and actuarial studies. However, there has been little recent work on the Gompertz in comparison with its early investigation. The problem of analyzing and estimating parameters of bivariate Gompertz distribution with shared frailty is of interest and the focus of this paper. We propose maximum likelihood estimation procedu...

Univariate Birnbaum-Saunders distribution has received a considerable amount of attention in recent years. Rieck and Nedelman (1991, ’A log-linear model for the Birnbaum-Saunders distribution’, Technometrics, 51-60) introduced a log BirnbaumSaunders distribution. The main aim of this paper is to introduce bivariate log Birnbaum-Saunders distribution. The proposed model is symmetric and it has f...

Marshall and Olkin (1997) provided a general method to introduce a parameter into a family of distributions, and discussed in details about the exponential and Weibull families. They have also briefly introduced the bivariate extension, although not any properties or inferential issues have been explored, mainly due to analytical intractability of the general model. In this paper we consider th...