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Results for "Probability Distributions on a Circle"

Subject: Benford's Law Departments: Department of Mathematical and Statistical Sciences

  • Approximation and invariance properties of one-dimensional probabilities

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    Fall 2018

    Xu,Chuang

    Approximation of probability measures, quantization, Kantorovich metric, Levy metric, Kolmogorov metric, Benford's Law, slowly changing sequences, asymptotic distribution, invariance property.","This thesis is based on four papers. The first two papers fall into the field of approximation of one

    upper estimate $\lt(N^{-1}\lt(\log N\rt)^{1/2}\rt)$ is obtained for the rate of convergence w.r.t. the Kantorovich metric on the circle. Moreover, a sharp rate of convergence $\lt(N^{-1}\log N\rt)$ w.r.t. the Kantorovich and the discrepancy (or Kolmogorov) metrics on the real line is derived. The last

    paper proves a threshold result on the existence of a circularly invariant and uniform probability measure (CIUPM) for non-constant linear transformations on the real line, which shows that there is a constant $c$ depending only on the slope of the linear transformation such that there exists a CIUPM if

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