Divergence-based robust inference for the Marshall-Olkin bivariate exponential distribution

Statistical modelling of bivariate data with ties is an active area of research. A widely used model for such data is the Marshall–Olkin bivariate exponential (MOBE) distribution. However, bivariate lifetime data often contain outliers, and the maximum likelihood estimator (MLE) for the MOBE model is highly sensitive to contamination. Therefore, robust parameter estimation is essential. In this article, we extend the minimum density power divergence estimation (MDPDE) method, proposed by Basu et al., to obtain robust and efficient estimation of the MOBE parameters. The MDPDE provides a robust generalization of the MLE while retaining good efficiency. We derive explicit estimating equations and establish the asymptotic distribution of the proposed estimators. The asymptotic relative efficiency is also investigated. The influence function of the MDPDE is bounded, ensuring robustness. A data–driven procedure for selecting the optimal tuning parameter is discussed. Simulation studies and a data application demonstrate the effectiveness of the proposed method overall.