$q$-probability distributions via an extension of the Bernoulli process
نویسندگان
چکیده
منابع مشابه
q-Probability: I. Basic Discrete Distributions
q-analogs of classical formulae go back to Euler, q-binomial coefficients were defined by Gauss, and q-hypergeometric series were found by E. Heine in 1846. The q-analysis was developed by F. Jackson at the beginning of the 20th century, and the modern point of view subsumes most of the old developments into the subjects of Quantum Groups and Combinational Enumeration. The general philosophy of...
متن کاملImproved Algorithms via Approximations of Probability Distributions
We present two techniques for constructing sample spaces that approximate probability distributions. The first is a simple method for constructing the small-bias probability spaces introduced by Naor and Naor. We show how to efficiently combine this construction with the method of conditional probabilities to yield improved parallel algorithms for problems such as set discrepancy, finding large...
متن کاملGeometry of q-Exponential Family of Probability Distributions
The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. W...
متن کاملGroup invariant inferred distributions via noncommutative probability
Abstract: One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance method for constructing inferred distributions on parameter spaces given observed results. These inferred distributions are obtained without using Ba...
متن کاملQ-Markov Random Probability Measures and Their Posterior Distributions
In this paper, we use the Markov property introduced in Balan and Ivanoff (2002) for set-indexed processes and we prove that a Markov prior distribution leads to a Markov posterior distribution. In particular, by proving that a neutral to the right prior distribution leads to a neutral to the right posterior distribution, we extend a fundamental result of Doksum (1974) to arbitrary sample spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0684648-5