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Estimation of the shape and scale parameters of the Weibull distribution. (English) Zbl 0111.15803
Summary: Estimates $$\hat c$$ and $$\hat b$$ 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: $$\hat c$$ obtained by first finding an estimate $$\hat d$$ of $$1/c$$, and then setting $$\hat c = 1/\hat d$$. When $$b$$ is unknown, $$\hat d$$ 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, $$\hat d$$ is an unbiased, non-negative and consistent estimate of $$d$$, and its efficiency is approximately 84%. An estimate $$\widehat{\log b}$$ of $$\log b$$ is found. Its asymptotic efficiency is 95%. It is proposed that $$\exp(\widehat{\log b})$$ be used to estimate $$b$$.

##### MSC:
 62-XX Statistics
statistics
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