Krzysztof Podgórski

Prefekt Statistiska institutionen, Professor

Laplace probability distributions and related stochastic processes

Författare

Tomasz Kozubowski
Krzysztof Podgorski

Redaktör

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.

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