A good simple percentile estimator of the weibull shape parameter for use when all three parameters are unknown

Stelios H. Zanakis and Nancy R. Mann

Naval Research Logistics Quarterly, 1982, vol. 29, issue 3, 419-428

Abstract: In this paper we consider a simple three‐order‐statistic asymptotically unbiased estimator of the Weibull shape parameter c for the case in which all three parameters are unknown. Optimal quantiles that minimize the asymptotic variance of this estimator, c̃ are determined and shown to depend only on the true (unknown) shape parameter value c and in a rather insensitive way. Monte Carlo studies further verified that, in practice where the true shape parameter c is unknown, using always c̃ with the optimal quantities that correspond to c = 2.0 produces estimates, c̃, remarkably close to the theoretical optimal. A second stage estimation procedure, namely recalculating c̃ based on the optimal quantiles corresponding to c̃, was not worth the additional effort. Benchmark simulation comparisons were also made with the best percentile estimator of Zanakis [20] and with a new estimator of Wyckoff, Bain and Engelhardt [18], one that appears to be the best of proposed closed‐form estimators but uses all sample observations. The proposed estimator, c̃, should be of interest to practitioners having limited resources and to researchers as a starting point for more accurate iterative estimation procedures. Its form is independent of all three Weibull parameters and, for not too large sample sizes, it requires the first, last and only one other (early) ordered observation. Practical guidelines are provided for choosing the best anticipated estimator of shape for a three‐parameter Weibull distribution under different circumstances.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:29:y:1982:i:3:p:419-428

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