A new estimator for Weibull distribution parameters: Comprehensive comparative study for Weibull Distribution

TL;DR

This paper introduces new $U$-statistics for estimating Weibull distribution parameters, proves their theoretical properties, and compares their performance with existing methods through simulations, showing superior bias performance for large samples.

Contribution

The paper proposes novel $U$-statistics for Weibull parameters, establishes their theoretical properties, and provides a comprehensive simulation-based comparison with existing estimators.

Findings

Proposed $U$-statistics are consistent and asymptotically normal.

$U$-statistics outperform existing estimators in bias for large samples.

Comprehensive simulation study validates the effectiveness of the new estimators.

Abstract

Weibull distribution has received a wide range of applications in engineering and science. The utility and usefulness of an estimator is highly subject to the field of practitioner's study. In practice users looking for their desired estimator under different setting of parameters and sample sizes. In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondary, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. Based on simulations, it turns out that the our proposed $U$-statistics show the best performance in terms of bias for estimating the shape and scale parameters when the sample size is large.