Atomic functions in nonparametric estimations of probability density functions and their derivatives

Nonparametric estimations of probability density function (PDF) [1-3] and its derivatives are considered. New constructions of weight functions (WF) [4, 5] with the compact support are offered and proved, allowing to build admissible estimations, both the density of probability and its derivatives 1st and 2nd orders. The numerical experiment and the physical analysis of its results confirm efficiency of nonparametric characteristics estimation of stochastic process.