The Block-Basu bivariate exponential (BBBE) distribution, see Block and Basu (1974), is one of the most popular variants of an absolutely continuous bivariate distribution. The traditional maximum likelihood estimation method is highly efficient, yet the maximum likelihood estimators (MLEs) can be significantly affected by the presence of a few outliers in the data. This article focuses on introducing a robust estimation procedure in the presence of outliers. We explore the implementation of the minimum density power divergence estimator (MDPDE) for robust and efficient parameter estimation of the BBBE distribution. The MDPDE is indexed by a single tuning parameter that controls the trade-off between robustness and efficiency. We show that the MDPDE for the BBBE model has a bounded influence function, that ensures the robustness of MDPDE. We compare the asymptotic covariance matrix of MDPDE with the Fisher information matrix. We study the asymptotic relative efficiency of MDPDE. We discussed about the data-driven selection of optimal tuning parameter. The simulation results indicate that the MDPDE is more robust and efficient than MLE for the BBBE distribution when outliers are present in a data set. A real data set has been analyzed for illustration purposes.
