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Rational characteristic functions and geometric infinite divisibility

Kozubowski, Tomasz J. and Podgorski, Krzysztof LU (2010) In Journal of Mathematical Analysis and Applications 365(2). p.625-637
Abstract
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Mixture of Laplace distributions, transform, Inverse Fourier, Skewed Laplace distribution, Geometric distribution, Convolution of exponential, distributions
in
Journal of Mathematical Analysis and Applications
volume
365
issue
2
pages
625 - 637
publisher
Elsevier
external identifiers
  • wos:000274351200019
  • scopus:74849135694
ISSN
0022-247X
DOI
10.1016/j.jmaa.2009.11.034
language
English
LU publication?
yes
id
6c85e0c8-e0e6-49ee-912d-7a7ea54e62bd (old id 1570116)
date added to LUP
2010-03-17 08:58:31
date last changed
2018-05-29 12:04:10
@article{6c85e0c8-e0e6-49ee-912d-7a7ea54e62bd,
  abstract     = {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.},
  author       = {Kozubowski, Tomasz J. and Podgorski, Krzysztof},
  issn         = {0022-247X},
  keyword      = {Mixture of Laplace distributions,transform,Inverse Fourier,Skewed Laplace distribution,Geometric distribution,Convolution of exponential,distributions},
  language     = {eng},
  number       = {2},
  pages        = {625--637},
  publisher    = {Elsevier},
  series       = {Journal of Mathematical Analysis and Applications},
  title        = {Rational characteristic functions and geometric infinite divisibility},
  url          = {http://dx.doi.org/10.1016/j.jmaa.2009.11.034},
  volume       = {365},
  year         = {2010},
}