Summary
Some of the many methods developed for estimating parameters or percentage points of the Weibull distribution are compared.
It is shown that the known estimation of the reciprocal shape parameter with the aid of a straight line in the extremal probability paper is rather biased for small sample sizes. To avoid the bias, correction factors are given, and the efficiency of the resulting unbiased estimator is calculated for sample sizesn=2, 3, …, 9.
Results ofJ. Lieblein concerning the double exponential distribution are slightly modified in order to get best linear unbiased estimators for parameters and for the logarithms of percentage points of the Weibull distribution. Other methods are shortly discussed and a median-unbiased estimator for the shape parameter is derived.
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Vogt, H. Zur Parameter- und Prozentpunktschätzung von Lebensdauerverteilungen bei kleinem Stichprobenumfang. Metrika 14, 117–131 (1969). https://doi.org/10.1007/BF02613646
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DOI: https://doi.org/10.1007/BF02613646