On the construction of bivariate exponential distributions with an arbitrary correlation coefficient

In this paper we use a concept of multivariate phase–type distributions to define a class of bivariate exponential distributions. This class has the following three appealing properties. Firstly, we may construct a pair of exponentially distributed random variables with any feasible correlation coefficient (also negative). Secondly, the class satisfies that any linear combination (projection) of the marginal random variables is a phase–type distributions, The latter property is potentially important for the development hypothesis testing in linear models. Thirdly, it is very easy to simulate the exponential random vectors.