An alternative distribution function estimation method using rational Bernstein polynomials

Abstract This paper gives a general method for nonparametric distribution function estimation using the rational Bernstein polynomials as an alternative to the current estimators. The proposed new method is compared with Bernstein polynomials and empirical distribution function methods by simulation studies. The new method guarantees monotone nondecreasing function by applying linear constraints on the coefficients of the rational Bernstein basis functions and smooth the empirical distribution function. Furthermore, as a special case, it reduces to Bernstein polynomial estimator method. Some theoretical properties of the new estimator are investigated. Simulation study shows that the proposed estimator is preferable to the Bernstein polynomials and empirical distribution function estimator methods.