Bayesian estimation of Unit-Weibull distribution based on dual generalized order statistics with application to the Cotton Production Data

TL;DR

This paper develops Bayesian estimators for the Unit Weibull distribution using dual generalized order statistics, applying approximation and simulation methods, and demonstrates their effectiveness through simulation and real cotton production data analysis.

Contribution

It introduces Bayesian estimation techniques for the Unit Weibull distribution based on dual generalized order statistics, incorporating various loss functions and applying them to real-world data.

Findings

Bayesian estimators perform well in simulations.

Different loss functions impact estimator performance.

Application to cotton data illustrates practical utility.

Abstract

The Unit Weibull distribution with parameters $\alpha$ and $\beta$ is considered to study in the context of dual generalized order statistics. For the analysis purpose, Bayes estimators based on symmetric and asymmetric loss functions are obtained. The methods which are utilized for Bayesian estimation are approximation and simulation tools such as Lindley, Tierney-Kadane and Markov chain Monte Carlo methods. The authors have considered squared error loss function as symmetric and LINEX and general entropy loss function as asymmetric loss functions. After presenting the mathematical results, a simulation study is conducted to exhibit the performances of various derived estimators. As this study is considered for the dual generalized order statistics that is unification of models based distinct ordered random variable such as order statistics, record values, etc. This provides flexibility in our results and in continuation of this, the cotton production data of USA is analyzed for both submodels of ordered random variables: order statistics and record values.