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

TL;DR

This work extends Bayesian inference for the two-parameter Unit-Weibull distribution within the dual generalized order statistics framework, unifying order statistics and lower-record models. It derives posterior inferences under independent Gamma priors for $\alpha$ and $\beta$ and computes Bayes estimators for $\alpha$, $\beta$, and $R(t)$ using three approaches: Lindley, Tierney-Kadane, and MCMC, under symmetric and asymmetric loss functions (SELF, LINEX, GE). Through both simulation and a Cotton Production Data case study, the authors show that estimators under LINEX and GE losses typically achieve lower risk than those under SELF, with TK and MCMC often outperforming Lindley, especially as sample size grows. The practical contribution lies in providing a flexible, unified Bayesian toolkit for UW inference under dgos, enabling reliable reliability-type analysis for complex ordered data and verifying applicability via real-world data fits and comparisons to standard distributions. The results demonstrate the utility of dgos in capturing diverse ordered-sample structures and show robust performance of Bayesian estimators across multiple loss criteria in both simulated and real data contexts.

Abstract

The Unit Weibull distribution with parameters $α$ and $β$ 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.

Figures (1)

• Figure 1: Plot of empirical and theoretical cdf