Copula-Based Bivariate Sine-Transformed Nakagami Distribution: Properties, Estimation, and Applications

Abstract

Modeling dependence in bivariate continuous data is fundamental in reliability, survival analysis, and environmental studies. In this paper, we propose a new copula-based bivariate sine-transformed Nakagami (CB–SSN) distribution by combining flexible sine-transformed Nakagami marginals with the Clayton copula to capture lower-tail dependence and nonlinear association structures. Key statistical properties of the proposed model are derived, including the joint and marginal distributions, moment expressions, dependence measures, and distributions of the minimum and maximum. Parameter estimation is performed via maximum likelihood, and a Monte Carlo simulation study is conducted to evaluate the finite-sample performance of the estimators. The results demonstrate that the estimators are consistent and asymptotically efficient, with bias and RMSE decreasing as the sample size increases. The applicability of the proposed model is illustrated using the faithful dataset. Comparative results based on log-likelihood, AIC, and BIC show that the CB–SSN model provides a better fit than the classical Clayton–Nakagami model. These findings highlight the flexibility and practical relevance of the proposed distribution for modeling dependent lifetime data.