Estimation of the Shape and Scale Parameters of the Weibull Distribution

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.