Work

A Flexible Bivariate Lifetime Model with Upper Bound: Theoretical Development and Lifetime Application

Year: 2025

Type: article

Abstract: This paper introduces the bivariate bounded Gompertz–log-logistic (BBGLL) distribution, a bounded bivariate lifetime model built by coupling two bounded Gompertz–log-logistic marginals through a Clayton copula with an independent dependence parameter. The proposed model effectively describes positively dependent lifetimes within finite support and accommodates increasing, decreasing, and bathtub-shaped hazard rates. Analytical expressions for the survival functions, hazard rate functions, and joint moments are derived, while measures of association such as Kendall’s tau, Spearman’s rho, and tail-dependence coefficients characterize the dependence structure. Parameters are estimated via maximum likelihood, inference functions for margins (IFM), and semi-parametric methods, with performance assessed through Monte Carlo simulations. A real-life data application illustrates the practical relevance of the model, showing that the BBGLL distribution achieves a superior goodness-of-fit relative to existing bivariate alternatives, highlighting its practical usefulness.

Source: Axioms

DOI: 10.3390/axioms14120930

Authors: Shuhrah Alghamdi, Tassaddaq Hussain, Hassan S. Bakouch, Maher Kachour

Institutions: Princess Nourah bint Abdulrahman University, Mirpur University of Science and Technology, Qassim University, Gulf University for Science & Technology

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Princess Nourah Bint Abdulrahman University