Iterated bivariate rayleigh distribution

Abstract

Abstract The Rayleigh distribution is one of the lifetime distributions and a special case from Weibull distribution. It has widely used in many fields in real life, finance, signal processing, and communications. Copulas are functions that join their one-dimensional marginal distribution functions which are uniform on the interval (0,1). The copula is an important tool for constructing families of bivariate distributions and it is measure of dependence between two variables since it allows us to separate the effect of dependence from the effects of the marginal distributions. In this paper, we derive iterated bivariate Rayleigh distribution using the concept of copula with discussion of some properties, like the cdf, pdf, conditional pdf's, conditional expectation, covariance and correlation coefficient.