Unit-Weibull Distribution: Different Method of Estimations

Abstract

Recently, the unit-Weibull (UW) distribution is used quite effectively in analyzing lifetime data. The main goal of this article is to investigate the performance of seven estimation methods, namely maximum likelihood (ML), least square (LS), weighted least square (WLS), Anderson-Darling (AD), right-tail Anderson-Darling (RAD), Cramer-von-Mises (CVM) and percentile (PCE) for parameter estimation. An extensive Monte Carlo simulation study is considered to compare the performances of these methods through biases and mean square errors (MSEs). The numerical results show that the PCE estimator has significantly smaller MSE value for different sample sizes and parameter values in most cases. In addition, the ML and LS estimators have lower bias values than the other estimators in general. Finally, a real data set is presented for illustrative purposes.