Inference of Half Logistic Geometric Distribution Based on Generalized Order Statistics

TL;DR

This paper derives properties of the half logistic geometric distribution within the generalized order statistics framework, and develops Bayesian estimation methods for its parameter using MCMC and Lindley approximations, with real data applications.

Contribution

It introduces new expressions for moments and joint distributions of the half logistic geometric distribution based on generalized order statistics, and proposes Bayesian estimators for its parameter.

Findings

Derived marginal and joint moment generating functions.

Developed Bayesian estimators using MCMC and Lindley methods.

Validated methods with real demographic and reliability data.

Abstract

As the unification of various models of ordered quantities, generalized order statistics act as a simplistic approach introduced in \cite{kamps1995concept}. In this present study, results pertaining to the expressions of marginal and joint moment generating functions from half logistic geometric distribution are presented based on generalized order statistics framework. We also consider the estimation problem of $\theta$ and provides a Bayesian framework. The two widely and popular methods called Markov chain Monte Carlo and Lindley approximations are used for obtaining the Bayes estimators.The results are derived under symmetric and asymmetric loss functions. Analysis of the special cases of generalized order statistics, \textit{i.e.,} order statistics is also presented. To have an insight into the practical applicability of the proposed results, two real data sets, one from the field of Demography and, other from reliability have been taken for analysis.