Sankhya: The Indian Journal of Statistics
2002, Volume 64, Series A, Pt. 1, pp. 156--166
BIVARIATE EXPONENTIAL DISTRIBUTIONS USING LINEAR STRUCTURES
SRIKANTH K. IYER, Indian Institute of Technology, Kanpur
D. MANJUNATH, Indian Institute of Technology, Bombay
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.
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