Estimation of Weibull Quantiles With Minimum Error in the Distribution Function

Abstract

In this article the optimalpoint estimator of a Weibull quantile is investigated where optimality is defined in terms of the minimum mean square error of the predicted distribution function. The general form of the estimator is K1/ĉ where , ĉ are the maximum likelihood estimators of the scale (b) and shape (c) parameters respectively. The optimal K is given for quantiles 0.01, 0.05, 0.10, 0.90, 0.95, 0.99 for random samples of size n = 20(10)100(100)300.

Also presented for each pair of the above quantiles and sample sizes is the estimator (of the form K1/ĉ which makes the predicted DF unbiased.

KEYWORDS:

• Quantile estimation
• Optimal Weibull quantile estimation
• Minimum error in predicted
• distribution function