On p-generalized elliptical random processes
K. Robert Müller, Wolf‐Dieter Richter · Journal of Statistical Distributions and Applications · 2019
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.