Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification

Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification

© 2016 by the Mathematical Association of Thailand. All rights reserved. A large number of efficient statistical methods have been designed for a frequent case when the distributions are normal (Gaussian). In practice, many probability distributions are not normal. In this case, Gaussian-based techn...

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Main Authors: Thongchai Dumrongpokaphan, Pedro Barragan, Vladik Kreinovich
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008395342&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55977
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-559772018-09-05T03:06:59Z Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification Thongchai Dumrongpokaphan Pedro Barragan Vladik Kreinovich Mathematics © 2016 by the Mathematical Association of Thailand. All rights reserved. A large number of efficient statistical methods have been designed for a frequent case when the distributions are normal (Gaussian). In practice, many probability distributions are not normal. In this case, Gaussian-based techniques cannot be directly applied. In many cases, however, we can apply these techniques indirectly – by first applying an appropriate transformation to the original variables, after which their distribution becomes close to normal. Empirical analysis of different transformations has shown that the most successful are the power transformations X → Xhand their modifications. In this paper, we provide a symmetry-based explanation for this empirical success. 2018-09-05T03:06:59Z 2018-09-05T03:06:59Z 2016-01-01 Journal 16860209 2-s2.0-85008395342 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008395342&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/55977
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Thongchai Dumrongpokaphan
Pedro Barragan
Vladik Kreinovich
Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
description © 2016 by the Mathematical Association of Thailand. All rights reserved. A large number of efficient statistical methods have been designed for a frequent case when the distributions are normal (Gaussian). In practice, many probability distributions are not normal. In this case, Gaussian-based techniques cannot be directly applied. In many cases, however, we can apply these techniques indirectly – by first applying an appropriate transformation to the original variables, after which their distribution becomes close to normal. Empirical analysis of different transformations has shown that the most successful are the power transformations X → Xhand their modifications. In this paper, we provide a symmetry-based explanation for this empirical success.
format Journal
author Thongchai Dumrongpokaphan
Pedro Barragan
Vladik Kreinovich
author_facet Thongchai Dumrongpokaphan
Pedro Barragan
Vladik Kreinovich
author_sort Thongchai Dumrongpokaphan
title Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
title_short Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
title_full Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
title_fullStr Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
title_full_unstemmed Empirically successful transformations from non-gaussian to close-to-gaussian distributions: Theoretical justification
title_sort empirically successful transformations from non-gaussian to close-to-gaussian distributions: theoretical justification
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85008395342&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55977
_version_ 1681424605958373376

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