Several studies find that return volatility of stocks tends to exhibit long-range dependence, heavy tailedness, and clustering. In this study, we use high-frequency data to empirically investigate whether a sample of stocks exhibit those characteristics. Because we do find those characteristics, as suggested by Rachev and Mittnik (2000) we employ self-similar processes to capture them in modeli...

We present a novel statistical model, the generalized-Gaussian-Rician (GG-Rician) distribution, for characterization of synthetic aperture radar (SAR) images. Since accurate models lead to better results in applications such as target tracking, classification, or despeckling, characterizing SAR images various scenes including urban, sea surface, agricultural is essential. The proposed model bas...

This paper introduces the general purpose Gaussian Transform, which aims at representing a generic symmetric distribution as an infinite mixture of Gaussian distributions. We start by the mathematical formulation of the problem and continue with the investigation of the conditions of existence of such a transform. Our analysis leads to the derivation of analytical and numerical tools for the co...

While the Matrix Generalized Inverse Gaussian (MGIG) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways of sampling from the distribution have not been carefully studied. In this paper, we show that the MGIG is unimodal, and the mode can be obtained by solving an Algebraic...

The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of samples from a complex GGD have not been well defined in the literature. In this study, we provide a thorough presentation of the complex-valued GGD by i) constructing the probability density funct...

We propose a generalized Gibbs sampler algorithm for obtaining samples approximately distributed from a high-dimensional Gaussian distribution. Similarly to Hogwild methods, our approach does not target the original Gaussian distribution of interest, but an approximation to it. Contrary to Hogwild methods, a single parameter allows us to trade bias for variance. We show empirically that our met...

This paper presents a parameterized version of the stochastic information gradient (SIG) algorithm, in which the error distribution is modeled by generalized Gaussian density (GGD), with location, shape, and dispersion parameters. Compared with the kernel-based SIG (SIGKernel) algorithm, the GGD-based SIG (SIG-GGD) algorithm does not involve kernel width selection. If the error is zero-mean, th...