ON THE JOINT DISTRIBUTION OF STUDENTIZED ORDER 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 April 9, 1992; revised February 15, 1993)

Abstract. In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf’s is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936, Biometrika, 28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly.

Key words and phrases: Exponential distribution, normal distribution, studentized order statistics.