Unit exponentiated Weibull model with applications

Abstract

Developing new effective statistical distributions tailored to model data on the unit interval is essential in modern data analysis. In this article, we propose a novel distribution on the unit interval, termed the unit exponentiated Weibull distribution, derived from the three-parameter exponentiated Weibull distribution. We will explore the key statistical properties of this new distribution and employ the maximum likelihood and least squares methods for parameter estimation. A simulation study is conducted to evaluate the performance of the maximum likelihood and least squares estimates. The simulation study demonstrates that the maximum likelihood method outperforms the least squares method in estimating the three parameters of the underlying model. To illustrate the practical utility of the proposed model, we analyze real-world datasets and compare its performance against other established distributions. The results show that the proposed model provides a superior fit to the competing models considered in the study.