Work

A bounded Lindley exponential model with applications to industrial engineering and epidemiological data

Year: 2025

Type: article

Abstract: The log-Lindley exponential (LLE), a bounded variant of the Lindley exponential distribution, is introduced using the inverse exponential transformation method. The LLE demonstrates significant flexibility, generating novel and well-known distributions with various parameters and providing support, including log-Lindley, Lindley, and two-parameter Lindley distributions, and exhibiting diverse density shapes, including right-skewed, approximately symmetric, left-skewed, decreasing, U-shaped, and increasing, while the hazard rate can be increasing, J-shaped, and bathtub-shaped. We explore several important statistical properties of the LLE model, including moments, entropy, quantile function, actuarial measures, mean residual life function, and stochastic orderings, which enhance its applicability in practical settings. Our study presents nine distinct frequentist strategies for estimating the model's parameters. In addition, the performance of the proposed estimation method is studied and evaluated through extensive numerical simulations. Finally, applications to real-world datasets from industrial engineering and epidemiology reveal the LLE model's practical utility and superiority, with it outperforming other existing models in terms of goodness-of-fit and flexibility.

Source: AIMS Mathematics

DOI: 10.3934/math.2025726

Authors: Ahmed M. T. Abd El-Bar, Ahmed R. El-Saeed, Ahmed M. Gemeay

Institutions: Tanta University, Imam Mohammad ibn Saud Islamic University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: Al-Imam Muhammad Ibn Saud Islamic University