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Computability of Probability Distributions and Distribution Functions Mori, Takakazu Tsujii, Yoshiki Yasugi, Mariko Computable probability distribution computable probability distribution function effective convergence of probability distributions 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Takakazu Mori and Yoshiki Tsujii and Mariko Yasugi 2009 Is Part Of OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/OASIcs.CCA.2009.2270 urn:nbn:de:0030-drops-22704 https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2270 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode