ON THE JOINT DISTRIBUTION OF GRUBBS’ STATISTICS

TEA-YUAN HWANG^{1} AND CHIN-YUAN HU^{2}

1Institute of Statistics, National Tsing Hua University, Hsinchu 30043, Taiwan, R.O.C.

2Department of Business Education, National Changhua University of Education, Changhua 50058, Taiwan, R.O.C.

(Received March 5, 1993; revised April 15, 1994)

Abstract. In this paper, the joint pdf’s of Grubbs’ statistics for normal and exponential populations are obtained; and relationship between the two pdf’s is established. New formulations of the first marginal pdf of Grubbs’ statistics for these two populations are given; the formulation of the exponential population case is a new one. Iterative formulas for the pdf of Grubbs’ statistics are also obtained.

Key words and phrases: Exponential distribution, Grubbs’ statistics, normal distribution.