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.

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