Parameter Estimations In A Minimum-Type Scheme

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 - F_i(x,θ_i)), We propose a simple method to estimate one of the parameters of θ_i. The sample size s is randomly subdivided into m equal subsamples, (each subsample of size k); the minimal value τ_q is found in each subsample and the estimator θ= Σ^m _q=1 τ_q/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.