Downton’s bivariate exponential distribution is one of the most important bivariate distributions in reliability theory. In this paper a simple representation for Downton’s bivariate exponential random vector is given. As an application of this representation, we consider a reliability model...

Motivated by hydrological applications, we derive the exact distributions of R=X + Y, P=XY and W=X/(X+Y) and the corresponding moment properties when X and Y follow Friday and Patil's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska....

The first known bivariate distribution with gamma and beta marginals is introduced. Various representations are derived for its joint probability density function (pdf), joint cumulative distribution function (cdf), product moments, conditional pdfs, conditional cdfs, conditional moments, joint...

We present recurrence relations for the moments of order statistics from the Topp–Leone distribution without any restriction for the shape parameter. Several relations are also derived when the shape parameter is an integer. An application of the results is provided.