 The standard kernel estimator formula_13 of formula_14 is

formula_15,

where formula_16 is the smoothing parameter.And the corresponding distribution function estimator formula_17 is

formula_18.Based on the assumption that original data set is realization of a random sample from a distribution of a specific parametric type, in this case a parametric model is fitted by parameter θ, often by maximum likelihood, and samples of random numbers are drawn from this fitted model.