Parameter Estimations In A Minimum-Type Scheme

L. Friedman, I. Gertsbakh

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This paper deals with parameter estimations when a sample is drawn from a population having a minimum-type distribution function (DF) G(x) = 1 - πn i=1 (1 - Fi(x,θi)), We propose a simple method to estimate one of the parameters of θi. The sample size s is randomly subdivided into m equal subsamples, (each subsample of size k); the minimal value τq is found in each subsample and the estimator θ= Σm q=1 τq/m is used. It turns out that under certain conditions concerning only the behavior of F1 (x,θ1) near x = 0, θ is an asymptotically unbiased (as k → ∞) and consistent (as s/k → ∞) estimator of only one unknown parameter, for example θ1. A numerical example based on simulation of 200 samples with s = 24, 48, 96 is considered for F1(x,θ1) - the exponential function and F2- the Weibull DF. The results of our method are summarized in Tables I-IV from which we deduce the characters of our estimator. We tried to improve our estimator θ1 by jackknifing, and show the improvement in a numerical example.

Original languageEnglish
Pages (from-to)439-462
Number of pages24
JournalCommunications in Statistics - Theory and Methods
Issue number5
StatePublished - 1 Jan 1981


  • Weibull distri-
  • bution
  • exponential distribution
  • jackknifing
  • minimum-type Scheme


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