Generalized Method of Moments and Percentile Method: Estimating parameters of the Novel Median Based Unit Weibull Distribution

TL;DR

This paper introduces GMM and percentile estimation methods for a new median-based unit Weibull distribution, addressing issues with traditional MLE and demonstrating their effectiveness through real data analysis.

Contribution

It presents novel GMM and percentile estimation techniques specifically designed for the median-based unit Weibull distribution, improving parameter estimation accuracy.

Findings

GMM and percentile methods outperform MLE in variance reduction

The methods successfully estimate parameters with real data

Enhanced estimation stability demonstrated

Abstract

The Median Based Unit Weibull is a new 2 parameter unit Weibull distribution defined on the unit interval (0,1). Estimation of the parameters using MLE encountered some problems like large variance. Using generalized method of moments (GMMs) and percentile method may ameliorate this condition. This paper introduces GMMs and the percentile methods for estimating the parameters of the new distribution with illustrative real data analysis.