Nonparametric estimation of bivariate cumulative distribution function

Abstract This paper proposes a nonparametric estimation of the cumulative distribution function of bivariate bounded data using the Birnbaum–Saunders kernel. We obtain its asymptotic properties and conduct a numerical study. The results demonstrate the superiority of the proposed estimator over the empirical distribution function and ordinary kernel estimator. We use the proposed estimator to analyse a real data set.