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Erschienen in:
Validating Markov Switching VAR Through Spectral Representations Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation

verfasst von : Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta

Erschienen in: Causal Inference in Econometrics

Verlag: Springer International Publishing

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Abstract

Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries—shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity x— then the resulting optimal families of probability distributions indeed include most of the empirically successful families. Thus, we get a symmetry-based explanation for their empirical success.

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Vorheriges Kapitel Invariance Explains Multiplicative and Exponential Skedactic Functions
Nächstes Kapitel The Multivariate Extended Skew Normal Distribution and Its Quadratic Forms
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Metadaten
Titel
Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation
verfasst von
Vladik Kreinovich
Olga Kosheleva
Hung T. Nguyen
Songsak Sriboonchitta
Copyright-Jahr
2016
Buch
Causal Inference in Econometrics

Print ISBN: 978-3-319-27283-2

Electronic ISBN: 978-3-319-27284-9

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-27284-9_8

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