Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 3, 399--406

CONCOMITANT OF ORDER STATISTICS IN GUMBEL'S BIVARIATE EXPONENTIAL DISTRIBUTION

By

K. BALASUBRAMANIAN
*Indian Statistical Insitute, New Delhi*

and

M.I. BEG
* University of Hyderabad, Hyderabad*

SUMMARY.For the Gumbel's bivariate exponential distribution, we find the distribution of the concomitant of the r-th order statistic of one of the components. Properties that concomitants get from the corresponding order statistics are used to derive a number of results. Recurrence relations between moments of concomitants are also obtained. Finally, we obtain the expression for the joint distribution of concomitants of two order statistics.

*AMS (1991) subject classification.* 62G30.

*Key words and phrases. *Gumbel's bivariate exponential
distribution, order statistics, concomitant, recurrence relations.