On Some Properties of Bivariate Exponential Distributions

Abstract

We show that the two bivariate exponential distributions constructed in Bladt and Nielsen^{[ 5 ]} have the maximum and minimum correlation coefficients for any given order. We also generalize their constructions to the case where the matrix representations of the two (marginal) exponential distributions have different orders and show that the new constructions also have the maximum and minimum correlation coefficients. Our main tool is a majorization result for a special set of PH-generators.

Keywords:

• Bivariate exponential distribution
• Correlation coefficient
• Majorization
• Multivariate distribution
• Phase-type distribution

Mathematics Subject Classification:

• Primary 62H05
• Secondary 60E10

ACKNOWLEDGMENT

We thank a referee and an editor for their valuable comments and suggestions.