Measurement Techniques

, Volume 59, Issue 6, pp 571–576 | Cite as

Nonparametric Estimate of a Parzen-Type Probability Density with an Implicitly Specified Form of the Kernel

  • A. V. Lapko
  • V. A. Lapko

A nonparametric estimate for the probability density is proposed with better approximation properties than the traditional Rosenblatt–Parzen statistics. The dependences of its properties on the form of the kernel function and on the formulas for the sampling interval for the random quantity are discussed.


probability density nonparametric Rosenblatt–Parzen estimate approximation properties kernel function Sturges’ rule Heinhold–Gaede formula 


This work was carried out within the framework of the project part of State Assignment of Ministry of Education and Science of Russia (No. 2.914.2014/K).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Computational ModellingSiberian Branch of the Russian Academy of SciencesKrasnoyarskRussia
  2. 2.Siberian State Aerospace UniversityKrasnoyarskRussia

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