Laplace probability distributions and related stochastic processes
Author
Editor
- Yuriy Shmaliy
Summary, in English
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.
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.
Department/s
Publishing year
2012
Language
English
Pages
105-145
Publication/Series
Probability: Interpretation, Theory and Applications
Document type
Book chapter
Publisher
Nova Science Publishers, Inc.
Topic
- Probability Theory and Statistics
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
Status
Published
ISBN/ISSN/Other
- ISBN: 978-1-62100-249-9