Computability of Probability Distributions and Distribution Functions

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.

• Type: Conference
• Year: 2009
• Where: CCA
• Authors: Takakazu Mori, Yoshiki Tsujii, Mariko Yasugi
• Keywords: CCA 2009, Distribution Functions, Effective Convergence, Probability Distributions, Theoretical Computer Science