Bivariate Inverse Topp-Leone Model to Counter Heterogeneous Data

TL;DR

This paper introduces a novel bivariate modeling approach combining FGM copula and inverse Topp-Leone distribution to effectively handle heterogeneity in lifetime data, supported by theoretical development and real data applications.

Contribution

It proposes a new bivariate model using FGM copula and inverse Topp-Leone distribution, with parameter estimation via MLE and Bayesian MCMC, addressing heterogeneity in data.

Findings

Model effectively captures heterogeneity in bivariate data

Application to Drought and Burr datasets demonstrates improved fit

Provides comprehensive theoretical and practical framework

Abstract

In probability and statistics, reliable modeling of bivariate continuous characteristics remains a real insurmountable consideration. During analysis of bivariate data, we have to deal with heterogeneity that is present in data. Therefore, for dealing with such a scenario, we investigate a novel technique based on a Farlie-Gumbel-Morgenstern (FGM) copula and the inverse Topp-Leone (ITL) model in this study. The idea is to use the oscillating functionalities of the FGM copula and the flexibility of the ITL model to propose a serious bivariate solution for the modeling of bivariate lifetime phenomena to counter the heterogeneity present in data. Both theory and practice are developed. In particular, we determine the main functions related to the model, like the cumulative model function, probability density function, conditional density function, and various useful dependence measures for bivariate modeling. The model parameters are estimated using the maximum likelihood method and Bayesian framework of Markov Chain Monte Carlo (MCMC) methodology. Following that, model comparison methods are used to compare models. To explain the findings and show that better models are recommended, the famous Drought and Burr data sets are used.