## Abstract

The problem of obtaining a numerical functional approximation of probability density on the basis of a given or simulated sample values with a prescribed error level at the minimum cost is considered. A computational algorithm for solving this problem that is a functional version of the kernel estimate of the probability density is proposed. This algorithm is similar to the functional computational kernel statistical algorithm for the approximate solution of the Fredholm integral equation of second kind, for which the theory of conditional optimization was earlier built. In this paper, this theory is built for the constructed functional computational kernel algorithm of approximating the probability density.

Translated title of the contribution | Условная оптимизация функционального вычислительного ядерного алгоритма приближения вероятностной плотности по заданной выборке |
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Original language | English |

Article number | 3 |

Pages (from-to) | 1401-1415 |

Number of pages | 15 |

Journal | Computational Mathematics and Mathematical Physics |

Volume | 61 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2021 |

## Keywords

- conditionally optimal parameters
- functional computational kernel algorithm
- functional computational statistical algorithm
- numerical approximation of functions
- numerical functional approximation of probability density

## OECD FOS+WOS

- 1.01 MATHEMATICS
- 1.03 PHYSICAL SCIENCES AND ASTRONOMY

## State classification of scientific and technological information

- 27.41 Computational mathematics