Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 156--166

BIVARIATE EXPONENTIAL DISTRIBUTIONS USING LINEAR STRUCTURES

By

SRIKANTH K. IYER, Indian Institute of Technology, Kanpur
D. MANJUNATH, Indian Institute of Technology, Bombay

and

R. MANIVASAKAN, Indian Institute of Technology, Bombay

SUMMARY. We derive bivariate exponential distributions using independent auxiliary random variables. We develop separate models for positive and negative correlations between the exponentially distributed variates. To obtain a positive correlation, we define a linear relation between the variates X and Y of the form Y=aX+Z where a is a positive constant and Z is independent of X. To obtain exponential marginals for X and Y we show that Z is a product of a Bernoulli and an Exponential random variables. To obtain negative correlations, we define X=aP+V and Y=bQ+W where either P and Q or V and W or both are antithetic random variables. For the case of positive correlations, we also characterize a bivariate Poisson process generated by using the bivariate exponential as the interarrival distribution

AMS (1991) subject classification. Primary 62E10, 62H05; secondary 62N05, 60K25, 62H20.

Key words and phrases. Bivariate exponential distribution, joint distribution, Laplace transform, correlation.

Full paper (PDF)