RECURRENCE RELATIONS FOR SINGLE AND PRODUCT MOMENTS OF PROGRESSIVE TYPE-II RIGHT CENSORED

ORDER STATISTICS FROM EXPONENTIAL AND TRUNCATED EXPONENTIAL DISTRIBUTIONS

RITA AGGARWALA AND N. BALAKRISHNAN

Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

(Received June 26, 1995; revised December 28, 1995)

Abstract. In this paper, we establish several recurrence relations satisfied by the single and product moments of progressive Type-II right censored order statistics from an exponential distribution. These relations may then be used, for example, to compute all the means, variances and covariances of exponential progressive Type-II right censored order statistics for all sample sizes n and all censoring schemes (R_{1}, R_{2}, …, R_{m}), m ≤ n. The results presented in the paper generalize the results given by Joshi (1978, Sankhyā Ser. B, 39, 362–371; 1982, J. Statist. Plann. Inference, 6, 13–16) for the single moments and product moments of order statistics from the exponential distribution.

To further generalize these results, we consider also the right truncated exponential distribution. Recurrence relations for the single and product moments are established for progressive Type-II right censored order statistics from the right truncated exponential distribution.

Key words and phrases: Progressive Type-II right censored order statistics, single moments, product moments, recurrence relations, exponential distribution, right truncated exponential distribution.