Comparing nonparametric density estimators using different canonical kernel functions

In this article we make a comparison between three different nonparametric density estimators .The first estimator is called fixed kernel which uses a fixed bandwidth.The second estimator is called variable kernel, which uses variable bandwidth, then the third estimator, refers to a new version of nonparametric density estimator (this estimator is a hybrid of the above estimators.This comparison depends on using different kernels, two of these functions are proposed in this article .To make this comparison suitable, we use standardization techniques, which are called canonical kernel.Simulation is used to find kernel function based on the standardization techniques (canonical kernel).