A New Bivariate Distribution with Rayleigh and Lindley Distributions as Marginals

Recently, a procedure of impounding a given marginal distribution, with the auxiliary density function generated from the assumed form of the distribution for the concomitant of an extreme order statistic of a sample, has been developed to create a bivariate distribution. In this paper we consider a marginal Rayleigh distribution and impound it with the pdf of an extended form of Lindley distribution to generate a new bivariate distribution. Some important properties of this new bivariate model together with some characterization theorems have been also derived. Most commonly used reliability functions associated with the generated bivariate distribution as well have been obtained. The well-known maximum likelihood (ML) method of estimation is applied for the estimation of the parameters of the generated bivariate distribution. A simulation study is also carried out to illustrate the closeness of ML estimates with the true value of the parameters. A real-life bivariate data set is used to demonstrate the application of the results of this paper in generating the appropriate bivariate distributional model in an innovative manner.