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Laplace probability distributions and related stochastic processes

Kozubowski, Tomasz and Podgorski, Krzysztof LU (2012) In Probability: Interpretation, Theory and Applications p.105-145
Abstract
Skew Laplace distributions, which naturally arise in connection with random summation

and quantile regression settings, offer an attractive and flexible alternative to

the normal (Gaussian) distribution in a variety of settings where the assumptions of

symmetry and short tail are too restrictive. The growing popularity of the Laplacebased

models in recent years is due to their fundamental properties, which include a

sharp peak at the mode, heavier than Gaussian tails, existence of all moments, infinite

divisibility, and, most importantly, random stability and approximation of geometric

sums. Since the latter arise quite naturally, these distributions provide useful... (More)
Skew Laplace distributions, which naturally arise in connection with random summation

and quantile regression settings, offer an attractive and flexible alternative to

the normal (Gaussian) distribution in a variety of settings where the assumptions of

symmetry and short tail are too restrictive. The growing popularity of the Laplacebased

models in recent years is due to their fundamental properties, which include a

sharp peak at the mode, heavier than Gaussian tails, existence of all moments, infinite

divisibility, and, most importantly, random stability and approximation of geometric

sums. Since the latter arise quite naturally, these distributions provide useful models

in diverse areas, such as biology, economics, engineering, finance, geosciences,

and physics. We review fundamental properties of these models, which give insight

into their applicability in these areas, and discuss extensions to time series, stochastic

processes, and random fields. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
vertical and horizontal asymmetry., stationary second order processes, subordination, selfsimilarity, random summation, random stability, quantile regression, parameter estimation, non-Gaussian moving average process, Mittag-Leffler distribution, microarray data analysis, geometric infinite divisibility, Linnink distribution, L´evy process, Laplace distribution, Bessel function distribution, geometric stable distribution
in
Probability: Interpretation, Theory and Applications
editor
Shmaliy, Yuriy
pages
105 - 145
publisher
Nova Science Publishers, Inc.
external identifiers
  • Scopus:84895277901
ISBN
978-1-62100-249-9
language
English
LU publication?
yes
id
1c40a92e-67e1-4fcd-b911-598ced683469 (old id 3049663)
date added to LUP
2012-09-10 12:40:19
date last changed
2016-10-13 04:46:49
@misc{1c40a92e-67e1-4fcd-b911-598ced683469,
  abstract     = {Skew Laplace distributions, which naturally arise in connection with random summation<br/><br>
and quantile regression settings, offer an attractive and flexible alternative to<br/><br>
the normal (Gaussian) distribution in a variety of settings where the assumptions of<br/><br>
symmetry and short tail are too restrictive. The growing popularity of the Laplacebased<br/><br>
models in recent years is due to their fundamental properties, which include a<br/><br>
sharp peak at the mode, heavier than Gaussian tails, existence of all moments, infinite<br/><br>
divisibility, and, most importantly, random stability and approximation of geometric<br/><br>
sums. Since the latter arise quite naturally, these distributions provide useful models<br/><br>
in diverse areas, such as biology, economics, engineering, finance, geosciences,<br/><br>
and physics. We review fundamental properties of these models, which give insight<br/><br>
into their applicability in these areas, and discuss extensions to time series, stochastic<br/><br>
processes, and random fields.},
  author       = {Kozubowski, Tomasz and Podgorski, Krzysztof},
  editor       = {Shmaliy, Yuriy},
  isbn         = {978-1-62100-249-9},
  keyword      = {vertical and horizontal asymmetry.,stationary second order processes,subordination,selfsimilarity,random summation,random stability,quantile regression,parameter estimation,non-Gaussian moving average process,Mittag-Leffler distribution,microarray data analysis,geometric infinite divisibility,Linnink distribution,L´evy process,Laplace distribution,Bessel function distribution,geometric stable distribution},
  language     = {eng},
  pages        = {105--145},
  publisher    = {ARRAY(0x8f846c8)},
  series       = {Probability: Interpretation, Theory and Applications},
  title        = {Laplace probability distributions and related stochastic processes},
  year         = {2012},
}