Let U and V be two independent normal random variables, and consider two new random variables X and Y of the form X = aU + bV, Y = cU + dV, where a, b, c, d, are some scalars. Each one of the random variables X and Y is normal, since it is a linear function of independent normal random variables.† Furthermore, because X and Y are linear functions of the same two independent normal random variab...

Recently it is observed that the generalized exponential distribution can be used quite effectively to analyze lifetime data in one dimension. The main aim of this paper is to define a bivariate generalized exponential distribution so that the marginals have generalized exponential distributions. It is observed that the joint probability density function, the joint cumulative distribution funct...

New uniform asymptotic approximations with error bounds are derived for a generalized total variation distance of Poisson approximations to the Poisson-binomial distribution. The method of proof is also applicable to other Poisson approximation problems. MSC 2000 Subject Classifications: Primary 62E17; secondary 60C05.

It has been argued in Arnold and Manjunath (2021) that the bivariate pseudo-Poisson distribution will be model of choice for data with one equidispersed marginal other over-dispersed. This is due to its simple structure, straightforward parameter estimation fast computation. In current note, we introduce effects concomitant variables on parameters explore distributional inferential aspects augm...