On the Construction of Bivariate Exponential Distributions with an Arbitrary Correlation Coefficient

Abstract

In this article we use the 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 distribution. The latter property is partially important for the development of hypothesis testing in linear models. Finally, it is easy to simulate the exponential random vectors.

Keywords:

• Arbitrary correlation
• Bivariate exponential distribution
• Matrix-exponential
• Phase-type distribution

Mathematics Subject Classification:

• Primary 62H05
• Secondary 60E10

ACKNOWLEDGMENTS

The authors are grateful for the support by Otto M⊘nsteds Foundation, the Danish Research Council for Technology and Production Sciences grant no. 247-07-0090, and Sistema Nacional de Investigadores, grant 15945.