RELATIONSHIPS BETWEEN MOMENTS OF TWO RELATED SETS OF ORDER STATISTICS AND SOME EXTENSIONS

N. BALAKRISHNAN^{1}, Z. GOVINDARAJULU^{2} AND K. BALASUBRAMANIAN^{3}

1Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S 4K1

2Department of Statistics, University of Kentucky, Lexington, KY 40506-0027, U.S.A. 3Indian Statistical Institute, SJS Sansanwal Marg, New Delhi 110016, India

(Received September 2, 1991; revised April 21, 1992)

Abstract. Govindarajulu expressed the moments of order statistics from a symmetric distribution in terms of those from its folded form. He derived these relations analytically by dividing the range of integration suitably into parts. In this paper, we establish these relations through probabilistic arguments which readily extend to the independent and non-identically distributed case. Results for random variables having arbitrary multivariate distributions are also derived.

Key words and phrases: Double exponential distribution, exponential distribution, order statistics, outliers, permanents, recurrence relations.