On p-generalized elliptical random processes

Klaus Müller and Wolf-Dieter Richter ()
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Klaus Müller: University of Rostock, Institute of Mathematics
Wolf-Dieter Richter: University of Rostock, Institute of Mathematics

Journal of Statistical Distributions and Applications, 2019, vol. 6, issue 1, 1-37

Abstract: Abstract We introduce rank-k-continuous axis-aligned p-generalized elliptically contoured distributions and study their properties such as stochastic representations, moments, and density-like representations. Applying the Kolmogorov existence theorem, we prove the existence of random processes having axis-aligned p-generalized elliptically contoured finite dimensional distributions with arbitrary location and scale functions and a consistent sequence of density generators of p-generalized spherical invariant distributions. Particularly, we consider scale mixtures of rank-k-continuous axis-aligned p-generalized elliptically contoured Gaussian distributions and answer the question when an n-dimensional rank-k-continuous axis-aligned p-generalized elliptically contoured distribution is representable as a scale mixture of n-dimensional rank-k-continuous p-generalized Gaussian distribution for a suitable mixture distribution of a positive random variable. Based on this class of multivariate probability distributions, we introduce scale mixed p-generalized Gaussian processes having axis-aligned finite dimensional distributions being p-generalizations of elliptical random processes. Additionally, some of their characteristic properties are discussed and approximates of trajectories of several examples such as p-generalized Student-t and p-generalized Slash processes having axis-aligned finite dimensional distributions are simulated with the help of algorithms to simulate rank-k-continuous axis-aligned p-generalized elliptically contoured distributions.

Keywords: Axis-aligned p-generalized elliptically contoured distributions; Density-like representation; Kolmogorov consistency conditions; p-generalized spherically invariant random processes; Scale mixtures of multivariate axis-aligned p-generalized elliptically contoured Gaussian distributions; Simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1186/s40488-019-0090-6

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