Median Based Unit Weibull Distribution (MBUW): Do the Higher Order Probability Weighted Moments (PWM) Add More Information over the Lower Order PWM in Parameter Estimation

TL;DR

This paper investigates whether higher order probability weighted moments provide more information than lower order moments in estimating parameters of the Median Based Unit Weibull distribution, using theoretical derivations and real data analysis.

Contribution

It compares the effectiveness of higher order versus lower order PWMs for parameter estimation in the MBUW distribution, including deriving the asymptotic distribution of the estimators.

Findings

Higher order PWMs can offer additional information for parameter estimation.

Asymptotic distribution of PWM estimators is derived.

Real data analysis illustrates the comparative performance.

Abstract

In the present paper, Probability weighted moments (PWMs) method for parameter estimation of the median based unit weibull (MBUW) distribution is discussed. The most widely used first order PWMs is compared with the higher order PWMs for parameter estimation of (MBUW) distribution. Asymptotic distribution of this PWM estimator is derived. This comparison is illustrated using real data analysis.