Series approximation to probability densities

机译：级数对概率密度的近似

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The standard Edgeworth and Gram-Charlier series expand a probability density. However if the series are truncated the resulting approximation to the probability density is generally not manifestly positive. We derive expansions of probability densities that when truncated are manifestly positive.

机译：标准Edgeworth和Gram-Charlier系列扩大了概率密度。但是，如果该系列被截断，则得出的概率密度近似值通常显然不是正数。我们得出了概率密度的扩展，该概率密度在被截断时显然是正的。

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《SPIE Defense + Security Conference》|2018年|106480C.1-106480C.9|共9页
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L. Cohen;
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Edgeworth series; Gram-Charlier series; manifestly positive series;

机译：Edgeworth系列;克·夏利尔系列;明显的正数;

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1. MULTILAYER PERCEPTRONS AS APPROXIMATIONS TO PROBABILITY DENSITY FUNCTIONS IN TIME SERIES FORECASTING [J] . JANUSZ MORAJDA Przeglad statystyczny . 2007,第1期

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2. Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme [J] . Applied numerical mathematics . 2020,第May期

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3. Adaptive noise variance identification for probability hypothesis density-based multi-target filter by variational bayesian approximations [J] . Radar, Sonar & Navigation, IET . 2013,第8期

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4. Manifestly positive series approximation to probability densities [C] . L. Cohen SPIE Defense + Commercial Sensing Conference . 2019

机译：明显正序列近似于概率密度
5. Approximations for skewed probability densities based on Laguerre series and biological applications. [D] . Lung, Te-Hsin. 1998

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6. Self-Consistent Density-Functional Embedding: A NovelApproach for Density-Functional Approximations [O] . Uliana Mordovina, *, ¶, -1

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7. Approximating Probability Densities by Iterated Laplace Approximations [O] . 2013

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8. Saddlepoint Approximations for the Combined Probability and Joint Probability Density Function of Selected Order Statistics and the Sum of the Remainder [R] . Nuttall, A. H. 2004

机译：选择顺序统计的组合概率和联合概率密度函数的鞍点近似与余数的和

Series approximation to probability densities

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