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Algorithms
Volume 18
Issue 8
10.3390/a18080466
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Analysis and Conditional Optimization of Projection Estimates for Distribution of Random Variable Using Legendre Polynomials

by
Tatyana Averina
1 and
Konstantin Rybakov
2,*
1
Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, 630090 Novosibirsk, Russia
2
Moscow Aviation Institute, National Research University, 125993 Moscow, Russia
*
Author to whom correspondence should be addressed.
Algorithms 2025, 18(8), 466; https://doi.org/10.3390/a18080466 (registering DOI)
Submission received: 7 June 2025 / Revised: 13 July 2025 / Accepted: 23 July 2025 / Published: 26 July 2025
(This article belongs to the Section Randomized, Online, and Approximation Algorithms)
Versions Notes

Abstract

Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of conditional optimization is solved. Such optimization allows one to increase the approximation accuracy with minimum computational costs. The proposed algorithms are tested on examples with different degrees of smoothness of the density. A projection estimate of the density is compared to a histogram that is often used in applications to estimate distributions.
Keywords: Monte Carlo method; projection estimate; density; distribution function; Legendre polynomials; conditional optimization Monte Carlo method; projection estimate; density; distribution function; Legendre polynomials; conditional optimization

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MDPI and ACS Style

Averina, T.; Rybakov, K. Analysis and Conditional Optimization of Projection Estimates for Distribution of Random Variable Using Legendre Polynomials. Algorithms 2025, 18, 466. https://doi.org/10.3390/a18080466

AMA Style

Averina T, Rybakov K. Analysis and Conditional Optimization of Projection Estimates for Distribution of Random Variable Using Legendre Polynomials. Algorithms. 2025; 18(8):466. https://doi.org/10.3390/a18080466

Chicago/Turabian Style

Averina, Tatyana, and Konstantin Rybakov. 2025. "Analysis and Conditional Optimization of Projection Estimates for Distribution of Random Variable Using Legendre Polynomials" Algorithms 18, no. 8: 466. https://doi.org/10.3390/a18080466

APA Style

Averina, T., & Rybakov, K. (2025). Analysis and Conditional Optimization of Projection Estimates for Distribution of Random Variable Using Legendre Polynomials. Algorithms, 18(8), 466. https://doi.org/10.3390/a18080466

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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