title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÑÐ½Ð¾Ð¹ Ð¾ÑÐµÐ½ÐºÐ¸ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ Ð¼Ð°Ð»Ð¾Ð¹ Ð²ÑÐ±Ð¾ÑÐºÐ¸: LââÐ¿Ð¾Ð´Ñ Ð¾Ð´
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Research on nuclear estimation of probability density in small sampling conditions: Lâ-approach
Creators: name: Ð¡Ð¾Ð±Ð¾Ð»ÐµÐ², ÐÐµÐ½Ð¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÑÐ°ÑÐ¸ÑÑÐ¸ÐºÐ°
Ð¡Ð»ÑÑÐ°Ð¹Ð½ÑÐµ Ð²ÐµÐ»Ð¸ÑÐ¸Ð½Ñ
ÑÐ´ÐµÑÐ½Ð°Ñ Ð¾ÑÐµÐ½ÐºÐ° Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸
Ð¾ÑÐµÐ½ÐºÐ° Ð Ð¾Ð·ÐµÐ½Ð±Ð»Ð°ÑÑÐ°
ÑÐ¸Ð¿ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ
Ð¼Ð°Ð»Ð°Ñ Ð²ÑÐ±Ð¾ÑÐºÐ°
nuclear estimation of probability density
Rosenblatt's estimation
type of distribution
small sample

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ´ÐµÑÐ½ÑÐ¼ Ð¾ÑÐµÐ½ÐºÐ°Ð¼ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸, Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð½ÑÐ¼ Ð¿Ð¾ Ð²ÑÐ±Ð¾ÑÐºÐ°Ð¼ ÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐ¼Ð° (Ð¼Ð°Ð»ÑÐ¼ Ð²ÑÐ±Ð¾ÑÐºÐ°Ð¼). ÐÑÐ½Ð¾Ð²Ð½Ð¾Ðµ Ð²Ð½Ð¸Ð¼Ð°Ð½Ð¸Ðµ ÑÐ´ÐµÐ»ÐµÐ½Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¾ÑÐµÐ½Ð¸Ð²Ð°Ð½Ð¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð² ÑÐ°Ð¼ÐºÐ°Ñ L1âÐ¿Ð¾Ð´ÑÐ¾Ð´Ð°, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð½Ð° Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¼ÐµÑÑ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¾ÑÐµÐ½ÐºÐ¸ ÐµÐµ Ð¸Ð½ÑÐµÐ³ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ (ÐÐ¡ÐÐ). ÐÑÐ¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÑÑÑ ÑÐ´ÐµÑÐ½Ð°Ñ Ð¾ÑÐµÐ½ÐºÐ° Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð Ð¾Ð·ÐµÐ½Ð±Ð»Ð°ÑÑÐ°-ÐÐ°ÑÐ·ÐµÐ½Ð° Ñ Ð¿Ð¾ÑÑÐ¾ÑÐ½Ð½ÑÐ¼ ÑÐ´ÑÐ¾Ð¼ Ð¸ ÑÑÐ¸ ÑÐ¸Ð¿Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ð¹ (Ð½Ð¾ÑÐ¼Ð°Ð»ÑÐ½Ð¾Ðµ, Ð¿Ð¾ÐºÐ°Ð·Ð°ÑÐµÐ»ÑÐ½Ð¾Ðµ Ð¸ ÑÐ°Ð²Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ðµ). ÐÑÐ»Ð¸ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÑÑ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐ²Ð»ÑÐµÑÑÑ Ð¾Ð±ÑÐ·Ð°ÑÐµÐ»ÑÐ½Ð¾Ðµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ðµ ÑÐºÐ°Ð·Ð°Ð½Ð½Ð¾Ð¹ Ð¾ÑÐµÐ½ÐºÐ¸ Ð´Ð»Ñ ÑÐ»ÑÑÐ°Ñ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ Ð¼Ð°Ð»ÑÑ Ð¾Ð±ÑÐµÐ¼Ð¾Ð² Ð²ÑÐ±Ð¾ÑÐºÐ¸. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ Ð¸Ð½ÑÐµÐ³ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÑÐµÐ´Ð½ÐµÐ³Ð¾ Ð°Ð±ÑÐ¾Ð»ÑÑÐ½Ð¾Ð³Ð¾ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ñ (ÐÐ¡ÐÐ) Ð¾Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ° ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ñ, ÑÐ¾ÑÐµÑÐ½ÑÐµ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð² ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ð¸ Ð´Ð»Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ° ÑÐ³Ð»Ð°Ð¶Ð¸Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð¼Ð¸Ð½Ð¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÐÐ¡ÐÐ Ð¸ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½Ñ Ð²ÑÐ²Ð¾Ð´Ñ.
description: The work is devoted to nuclear estimates of probability density, which are built from samples of final volume (small samples). The main focus is obtaining of the results of the probability density assessment in the L1âapproach, which is based on the using of its integrated mean absolute deviation (IMAD) as a measure of accuracy. The research uses a nuclear estimate of the Rosenblatt-Parsen probability density with a constant nucleus and three types of distributions (normal, indicative and uniform). A distinctive feature of setting the task is the mandatory consideration of this estimate for the case of finite small sample volumes. As a result, dependencies were obtained and data graphs were constructed for integrated mean absolute deviation (IMAD) from the smoothing parameter, point graphs of dependence as a result of interpolation were counted for the optimal smoothing parameter and minimum IMAD, and conclusions were given.