Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces Article Swipe

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TrungTin Nguyen , Faïcel Chamroukhi , Hien D. Nguyen , Geoffrey J. McLachlan ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.1080/03610926.2021.2002360

The class of location-scale finite mixtures is of enduring interest both from\napplied and theoretical perspectives of probability and statistics. We prove\nthe following results: to an arbitrary degree of accuracy, (a) location-scale\nmixtures of a continuous probability density function (PDF) can approximate any\ncontinuous PDF, uniformly, on a compact set; and (b) for any finite $p\\ge1$,\nlocation-scale mixtures of an essentially bounded PDF can approximate any PDF\nin $\\mathcal{L}_{p}$, in the $\\mathcal{L}_{p}$ norm.\n

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Lebesgue integration Mathematics Probability density function Bounded function Scale (ratio) Norm (philosophy) Probability measure Class (philosophy) Finite set Set (abstract data type) Probability distribution Discrete mathematics Applied mathematics Mathematical analysis Statistics Computer science Physics Artificial intelligence Political science Law Quantum mechanics Programming language

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Type: article
Language: en
Landing Page: https://doi.org/10.1080/03610926.2021.2002360
OA Status: green
Cited By: 13
References: 26
Related Works: 10
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DOI: https://doi.org/10.1080/03610926.2021.2002360

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Title: Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces

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Language: en

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Publication year: 2022

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Publication date: 2022-05-26

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Authors: TrungTin Nguyen, Faïcel Chamroukhi, Hien D. Nguyen, Geoffrey J. McLachlan

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Landing page: https://doi.org/10.1080/03610926.2021.2002360

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Concepts: Lebesgue integration, Mathematics, Probability density function, Bounded function, Scale (ratio), Norm (philosophy), Probability measure, Class (philosophy), Finite set, Set (abstract data type), Probability distribution, Discrete mathematics, Applied mathematics, Mathematical analysis, Statistics, Computer science, Physics, Artificial intelligence, Political science, Law, Quantum mechanics, Programming language

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Cited by: 13

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