Asymmetric Kernel Density Estimator for Length BiasedData.

This article considers smooth density estimation based on length biased data that involves a random sample based on a nonnegative random variable (r.v.) having a continuous probability density function (pdf) g(x) that is proportional to another density f(x) weighted by a weight function w(x). The density f(x) is of interest. In the present article we investigate the adaptation of asymmetric kernel estimator proposed and studied in Chaubey, Sen and Sen (2007, Technical Report 01/07, Department of Mathematics & Statistics, Concordia University) through smoothing of the usual empirical distribution function and the Cox's estimator. Our simulation study demonstrates that the asymmetric kernel estimators proposed here are good competitors to other estimators.