Estimation of parameters of the logistic exponential distribution under progressive type-I hybrid censored sample

TL;DR

This paper develops methods for estimating parameters of the logistic exponential distribution from censored data, using maximum likelihood and Bayesian approaches, with numerical techniques and real data illustration.

Contribution

It introduces Bayesian estimation under various loss functions and employs Lindley's approximation and importance sampling for complex posterior calculations.

Findings

Maximum likelihood estimates obtained via Newton-Raphson method.

Bayesian estimates derived under squared error, LINEX, and entropy loss functions.

Interval estimates and credible intervals constructed for the parameters.

Abstract

The paper addresses the problem of estimation of the model parameters of the logistic exponential distribution based on progressive type-I hybrid censored sample. The maximum likelihood estimates are obtained and computed numerically using Newton-Raphson method. Further, the Bayes estimates are derived under squared error, LINEX and generalized entropy loss functions. Two types (independent and bivariate) of prior distributions are considered for the purpose of Bayesian estimation. It is seen that the Bayes estimates are not of explicit forms.Thus, Lindley's approximation technique is employed to get approximate Bayes estimates. Interval estimates of the parameters based on normal approximate of the maximum likelihood estimates and normal approximation of the log-transformed maximum likelihood estimates are constructed. The highest posterior density credible intervals are obtained by using the importance sampling method. Furthermore, numerical computations are reported to review some of the results obtained in the paper. A real life dataset is considered for the purpose of illustrations.