Median Based Unit Weibull (MBUW) A New Unit Distribution: Comparisons Between Variants of Generalized Methods of Moments and Percentile Estimator

This paper introduces a new two-parameter unit Weibull distribution defined on the interval (0,1). It discusses the methodology for deriving its probability density function (PDF), explores various properties, and presents related functions. Numerous figures illustrate the distribution and demonstrate its effectiveness in fitting a wide range of skewed real data. The parameter estimation process using maximum likelihood estimation (MLE) faced challenges, particularly concerning large variance. To address these issues, the generalized method of moments (GMMs) and percentile estimators are introduced as improved alternatives. The paper elaborates on GMMs, percentile estimators, and new variants of both methods for estimating the parameters of the new distribution, supplemented by illustrative analyses of real data.