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Rational characteristic functions and geometric infinite divisibility

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Author

Summary, in English

Motivated by the fact that exponential and Laplace distributions have rational characteristic functions and are both geometric infinitely divisible (GID), we investigate the latter property in the context of more general probability distributions on the real line with rational characteristic functions of the form P(t)/Q (t), where P(t) = 1 + a(1)it + a(2)(it)(2) and Q (t) = 1 + b(1)it + b(2)(it)(2). Our results provide a complete characterization of the class of characteristic functions of this form, and include a description of their GID subclass. In particular, we obtain characteristic functions in the class and the subclass that are neither exponential nor Laplace. (C) 2009 Elsevier Inc. All rights reserved.

Publishing year

2010

Language

English

Pages

625-637

Publication/Series

Journal of Mathematical Analysis and Applications

Volume

365

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Probability Theory and Statistics

Keywords

  • Mixture of Laplace distributions
  • transform
  • Inverse Fourier
  • Skewed Laplace distribution
  • Geometric distribution
  • Convolution of exponential
  • distributions

Status

Published

ISBN/ISSN/Other

  • ISSN: 0022-247X