Computability of Probability Distributions and Distribution Functions

Authors Takakazu Mori, Yoshiki Tsujii, Mariko Yasugi



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Takakazu Mori
Yoshiki Tsujii
Mariko Yasugi

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Takakazu Mori, Yoshiki Tsujii, and Mariko Yasugi. Computability of Probability Distributions and Distribution Functions. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 185-196, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/OASIcs.CCA.2009.2270

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.
Keywords
  • Computable probability distribution
  • computable probability distribution function
  • effective convergence of probability distributions

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