Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/195888 
Year of Publication: 
2017
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 5 [Issue:] 3 [Publisher:] MDPI [Place:] Basel [Year:] 2017 [Pages:] 1-17
Publisher: 
MDPI, Basel
Abstract: 
For evaluating the probabilities of arbitrary random events with respect to a given multivariate probability distribution, specific techniques are of great interest. An important two-dimensional high risk limit law is the Gauss-exponential distribution whose probabilities can be dealt with based on the Gauss-Laplace law. The latter will be considered here as an element of the newly-introduced family of (p,q) -spherical distributions. Based on a suitably-defined non-Euclidean arc-length measure on (p,q) -circles, we prove geometric and stochastic representations of these distributions and correspondingly distributed random vectors, respectively. These representations allow dealing with the new probability measures similarly to with elliptically-contoured distributions and more general homogeneous star-shaped ones. This is demonstrated by the generalization of the Box-Muller simulation method. In passing, we prove an extension of the sector and circle number functions.
Subjects: 
Gauss-exponential distribution
Gauss–Laplace distribution
stochastic vector representation
geometricmeasure representation
(p, q)-generalized polar coordinates
(p, q)-arc length
dynamic intersection proportion function
(p, q)-generalized Box–Muller simulation method
(p, q)-spherical uniform distribution
dynamic geometric disintegration
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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