Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH scholarly article en Mori, Takakazu; Tsujii, Yoshiki; Yasugi, Mariko http://www.dagstuhl.de/oasics License
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URN: urn:nbn:de:0030-drops-22704
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Contributed Papers

Computability of Probability Distributions and Distribution Functions

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Abstract

We define the computability of probability distributions on the real line as well as that of distribution functions. Mutual relationships between the computability notion of a probability distribution and that of the corresponding distribution function are discussed. It is carried out through attempts to effectivize some classical fundamental theorems concerning probability distributions. We then define the effective convergence of probability distributions as an effectivization of the classical vague convergence. For distribution functions, computability and effective convergence are naturally defined as real functions. A weaker effective convergence is also defined as an effectivization of pointwise convergence.

BibTeX - Entry

@InProceedings{mori_et_al:OASIcs:2009:2270,
  author =	{Takakazu Mori and Yoshiki Tsujii and Mariko Yasugi},
  title =	{{Computability of Probability Distributions and Distribution Functions}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  series =	{OpenAccess Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2270},
  URN =		{urn:nbn:de:0030-drops-22704},
  doi =		{http://dx.doi.org/10.4230/OASIcs.CCA.2009.2270},
  annote =	{Keywords: Computable probability distribution, computable probability distribution function, effective convergence of probability distributions}
}

Keywords: Computable probability distribution, computable probability distribution function, effective convergence of probability distributions
Seminar: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue date: 2009
Date of publication: 2009


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