Paulaauskas, Vygantas Rachev, Svetlozar T.
Published in
Statistical Papers

In this paper we consider the problem of maximum likelihood (ML) estimation in the classical AR(1) model with i.i.d. symmetric stable innovations with known characteristic exponent and unknown scale parameter. We present an approach that allows us to investigate the properties of ML estimators without making use of numerical procedures. Finally, we...

Anh, V. V. Leonenko, N. N.
Published in
Journal of Statistical Physics

We present a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition. Gaussian and non-Gaussian limiting distributions of the renormalized solution of the fractional-in-time and in-space kinetic equation are described in terms of multiple stoc...

Tsionas, Efthymios G.
Published in
Statistical Papers

The purpose of the paper, is to explain how recent advances in Markov Chain Monte Carlo integration can facilitate the routine Bayesian analysis of the linear model when the prior distribution is completely user dependent. The method is based on a Metropolis-Hastings algorithm with a Student-t source distribution that can generate posterior moments...

Sato, Ken-iti Yamamuro, Kouji
Published in
Acta Applicandae Mathematica

For any stable distribution μ on the line, recurrence-transience of the selfsimilar additive process {Xt, t≥0} with ℒ(X1)=μ is determined. Comparison with the stable Lévy process {Yt, t≥0} with ℒ(Y1)=μ is made: if μ is not strictly stable, then {Yt} is transient but {Xt} is recurrent except the obviously transient case of monotone sample functions....

Tsoukatos, Konstantinos P. Makowski, Armand M.
Published in
Queueing Systems

We study the heavy traffic regime of a discrete-time queue driven by correlated inputs, namely the M/G/∞ input processes of Cox. We distinguish between M/G/∞ processes with short- and long-range dependence, identifying in each case the appropriate heavy traffic scaling that results in a nondegenerate limit. As expected, the limits we obtain for sho...

Avram, Florin Taqqu, Murad S.
Published in
Statistical Inference for Stochastic Processes

The R / S statistic is used to detect long-range dependence in a time series and to estimate its intensity. One of its virtues is robustness against different distributions. We show here that the R / S statistic continues to be robust if the time series is a moving average with long-range dependence with innovations that are in the domain of attrac...

Manatunga, Amita K. Oakes, David
Published in
Lifetime Data Analysis

Hougaard's (1986) bivariate Weibull distribution with positive stable frailties is applied to matched pairs survival data when either or both components of the pair may be censored and covariate vectors may be of arbitrary fixed length. When there is no censoring, we quantify the corresponding gain in Fisher information over a fixed-effects analysi...

Spătaru, Aurel
Published in
Journal of Theoretical Probability

Let X, X1, X2,... be a sequence of i.i.d. random variables such that EX=0, assume the distribution of X is attracted to a stable distribution with exponent α

Hughes, B D Shlesinger, M F Montroll, E W
Published in
Proceedings of the National Academy of Sciences of the United States of America

We construct a random walk on a lattice having a hierarchy of self-similar clusters built into the distribution function of allowed jumps. The random walk is a discrete analog of a Lévy flight and coincides with the Lévy flight in the continum limit. The Fourier transform of the jump distribution function is the continuous nondifferentiable functio...