Work

The Bivariate Inverted Topp–Leone Distribution: Distributional Properties and Statistical Inference

Year: 2026

Type: article

Abstract: In this article, we propose a new bivariate generalization of the inverted Topp–Leone distribution. First, we express its joint cumulative distribution and survival functions in series forms using special functions, which yields the bivariate hazard rate, reversed hazard rate, and the exact distributions of min{X,Y}. We then establish several essential properties, such as marginal and conditional distributions, joint moments, entropy, and the Fisher information matrix. After proving that the distribution exhibits positive likelihood ratio dependence, we derive the exact distributions for the transformations X+Y, X/(X+Y), and XY when X and Y follow an inverted bivariate Topp–Leone distribution. Finally, we round out the statistical framework by presenting parameter estimation techniques, a simulation study, and Bayesian inference.

Source: Mathematics

DOI: 10.3390/math14173199

Authors: Daya K. Nagar, Edwin Zarrazola, Santiago Echeverri-Valencia

Institution: Universidad de Antioquia

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Universidad de Antioquia