Preprint Article Version 1 This version not peer reviewed

The Class of (p,q)-spherical Distributions

Version 1 : Received: 18 July 2017 / Approved: 19 July 2017 / Online: 19 July 2017 (04:35:06 CEST)

A peer-reviewed article of this Preprint also exists.

Richter, W.-D. The Class of (p,q)-spherical Distributions with an Extension of the Sector and Circle Number Functions. Risks 2017, 5, 40. Richter, W.-D. The Class of (p,q)-spherical Distributions with an Extension of the Sector and Circle Number Functions. Risks 2017, 5, 40.

Journal reference: Risks 2017, 5, 40
DOI: 10.3390/risks5030040

Abstract

For evaluating 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 upon the Gauss-Laplace law. The latter will be considered here as an element of the newly introduced family of (p,q)-spherical distributions. Based upon 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 like with elliptically contoured distributions and more general homogeneous star-shaped ones. This is demonstrated at hand of a generalization of the Box-Muller simulation method. En passant, we prove an extension of the sector and circle number functions.

Subject Areas

Gauss-exponential distribution; Gauss-Laplace distribution; stochastic vector representation; geometric measure 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

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