A new approach to estimate parameters of the two-parameter Weibull distribution

Abstract

This study proposes a new approach to estimate the parameters of the two-parameter Weibull distribution in the case of complete (uncensored) or doubly Type II censored samples. The proposed estimators have closed forms and can be adapted to Type II right or Type II left censored samples. The new estimators are strongly consistent and the new shape estimator follows asymptotically a normal and the new scale estimator a lognormal distribution. Bias, mean square and efficiency performance of the new estimators are investigated through simulations and compared to some known estimation methods such as maximum likelihood estimation, method of moments, quantile estimation, maximum goodness of fit estimation, L-moments, U-statistics and bias-corrected maximum likelihood. According to the simulations, the newly proposed estimators seem to have good efficiency performance in comparison to the other methods, particularly in small samples. Furthermore, two real data sets are used to illustrate the new estimators.

Keywords:

• Weibull distribution; doubly Type II censoring; parameter estimation; order statistics

2020 Mathematics Subject Classification:

• Primary 62F10, Secondary 62G30, 62N05

Acknowledgements

The author would like to thank the Associate Editor and the two referees for their careful reading and for their comments that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

The data sets analyzed in the current study are included in the article.