Estimation of the Shape and Scale Parameters of the Weibull Distribution

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Abstract
Estimates ĉ and are proposed for the shape parameter c and the scale parameter b of the Weibull distribution on the assumption that the location parameter is known: ĉ obtained by first finding an estimate of 1/c, and then setting ĉ = 1/ . When b is unknown, is a consistent and non-negative estimate of d, with a bias which tends to vanish as the sample size increases and with an asymptotic efficiency of about 55%. When b is known, is an unbiased, non-negative and consistent estimate of d, and its efficiency is approximately 84%. An estimate In∧b of In b is found. Its asymptotic efficiency is 95%. It is proposed that exp(In∧b) be used to estimate b.

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