DEVELOPMENT OF BIVARIATE INVERTED NADARAJAH HAGHIGHI DISTRIBUTIONS: COPULA APPROACH

Abstract

Bivariate lifetime models are crucial in reliability analysis and survival research, necessitating flexible marginal distributions and dependence structures to accurately depict real-world data. This paper introduces a family of five-parameter bivariate distributions derived from the Inverted Nadarajah–Haghighi distribution by the use of copula functions, motivated by the inadequacies of current bivariate models in representing varied dependence structures. The Farlie–Gumbel–Morgenstern (FGM) and Plackett copulas are utilized to model the dependent structure.The primary objective of this work is to develop these new bivariate models, investigate their statistical properties, and assess the efficiency of parameter estimation methods. Parameters are estimated using Maximum Likelihood Estimation (MLE) and the Inference Function for Margins (IFM) approach, and the efficiency of the two methods is compared. The results indicate that MLE provides more efficient estimation of the copula parameter for both the FGM and Plackett copulas.To illustrate the applicability of the proposed models, two real data sets are analyzed. The findings show that the Bivariate Inverted Nadarajah–Haghighi distribution based on the Plackett copula offers a better fit than the corresponding model based on the FGM copula. Further comparison with the Bivariate Generalized Exponential Distribution reveals that while the latter performs better under the FGM copula, the proposed model under the Plackett copula outperforms it, yielding lower AIC and BIC values. These results demonstrate the flexibility and practical relevance of the proposed models for analyzing dependent lifetime data.