Estimation of the Location and Scale Parameters of Generalized Pareto Distribution Based on Progressively Type-II Censored Order Statistics

Abstract

Based on progressively type-II right censored order statistics, we establish several recurrence relations for the single and product moments from the generalized Pareto distribution due to Pikands (1975). Further, recursive computational algorithm is provided which enable us to compute all the means, variances and covariances for all sample sizes n, effective sample sizes m, and all progressive censoring schemes $$(R_{1},\ldots , R_{m})$$. These relations generalize the results given by Aggarwala and Balakrishnan (Ann Inst Stat Math 48:757–771, 1996) and Joshi (Sankhyd Set B 39:362–371, 1978) for standard exponential distribution. Besides, these moments are then utilized to derive best linear unbiased estimators (BLUEs) of the scale and location parameters of the generalized Pareto distribution. Next, we obtain the maximum likelihood estimators of the unknown parameters of the model under progressively type-II right censored order statistics. Monte Carlo simulations are performed to compare the performances of the proposed method, and a numerical example is presented to illustrate the method developed here to obtain BLUEs.