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A family of minimum quantile distance estimators for the three-parameter Weibull distribution

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Abstract

A family of minimum quantile distance estimators, based on a subset of the sample quantiles, is proposed for the parameters of the three-parameter Weibull distribution. The estimation procedure is applicable to either complete or censored samples and, through use of the associated distance measure, provides a goodness-of-fit test for the Weibull model. The proposed estimators are both consistent and asymptotically normal and, in a particular instance, are optimal over the class of all estimators based on the same quantile subset. The problem of optimal quantile selection is also considered.

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Authors and Affiliations

  1. Deparment of Statistics, Southern Methodist University, 75275, Dallas, Texas, USA

    T. J. Carmody & R. L. Eubank

  2. Department of Mathematical Sciences, University of Delaware, 19711, Newark, Delaware, USA

    V. N. LaRiccia

Authors
  1. T. J. Carmody
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  2. R. L. Eubank
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  3. V. N. LaRiccia
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Additional information

Research supported by the Office of Naval Research under contract number N00014-82-K-0207.

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Carmody, T.J., Eubank, R.L. & LaRiccia, V.N. A family of minimum quantile distance estimators for the three-parameter Weibull distribution. Statistische Hefte 25, 69–82 (1983). https://doi.org/10.1007/BF02932392

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