The Inverse Weighted Lindley Distribution: Properties, Estimation and an Application on a Failure Time Data

TL;DR

This paper introduces the inverse weighted Lindley distribution, exploring its mathematical properties, estimation methods, bias correction techniques, and demonstrating its application on failure time data.

Contribution

The paper proposes a new flexible distribution for modeling hazard rates, with detailed properties, estimation procedures, bias corrections, and real data application.

Findings

Distribution effectively models upside-down bathtub hazard rates

Bias correction methods improve estimator accuracy

Application demonstrates practical utility of the distribution

Abstract

In this paper a new distribution is proposed. This new model provides more flexibility to modeling data with upside-down bathtub hazard rate function. A significant account of mathematical properties of the new distribution is presented. The maximum likelihood estimators for the parameters in the presence of complete and censored data are presented. Two corrective approaches are considered to derive modified estimators that are bias-free to second order. A numerical simulation is carried out to examine the efficiency of the bias correction. Finally, an application using a real data set is presented in order to illustrate our proposed distribution.