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Estimating survivor function using optimally selected order statistics

Authors:	Prof K M Hassanein A K Md E Saleh E F Brown

Institution:	(1) The University of Kansas, College of Health Sciences and Hospital, 39th and Rainbow Blvd., 66103 Kansas City, Kansas, USA;(2) Carleton University, Ottawa;(3) Kansas University Medical Center, Kansas City

Abstract:	This paper deals with the estimation of survivor function $S_0 (t) = 1 - F_0 \left( {\frac{{t - \mu }}{\sigma }} \right)$ using optimally selected order statistics when the sample sizen is large. We use the estimates (μ,σ) based on the optimum set of order statistics $\{ x_{(n_1 )} ,x_{(n_2 )} ,...x_{(n_k )} \}$ for largen and fixedk (≤n) such that the estimate $S(t) = 1 - F_0 \left( {\frac{{t - \mu }}{{\sigma *}}} \right)$ has optimum variance property. The asymptotic relative efficiency of such an estimator is compared with the one based on the complete sample. The general theory of the problem and specific details with respect to a two-parameter Normal, Logistic, Exponential and Pareto distributions is considered as an example.

Keywords:	Location-scale family Survivor function Optimum order statistics Normal distribution Logistic distribution Pareto distribution Exponential distributions ARE (asymptotic relative efficiency) AARE (average asymptotic efficiency) ABLUE (asymptotic best linear unbiased estimate)
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