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In this paper, we study the asymptotic behavior of the kernel bivariate distribution function estimator for negatively superadditive dependent. The exponential convergence rates for the kernel estimator are investigated. Under certain regularity conditions, the optimal bandwidth rate is determined with respect to mean squared error criteria. A simulation study is used to justify the behavior of the kernel and histogram estimators. As an application, a real data set in hydrology is considered and the kernel bivariate distribution function estimator of the data is investigated.

Exponential convergence rates for the kernel bivariate distribution function estimator under NSD assumption with application to hydrology data