Properties and numerical evaluation of the Rosenblatt distribution
Abstract
This paper studies various distributional properties of the Rosenblatt distribution. We begin by describing a technique for computing the cumulants. We then study the expansion of the Rosenblatt distribution in terms of shifted chi-squared distributions. We derive the coefficients of this expansion and use these to obtain the L\'{e}vy-Khintchine formula and derive asymptotic properties of the L\'{e}vy measure. This allows us to compute the cumulants, moments, coefficients in the chi-square expansion and the density and cumulative distribution functions of the Rosenblatt distribution with a high degree of precision. Tables are provided and software written to implement the methods described here is freely available by request from the authors.
Keywords
Cite
@article{arxiv.1307.5990,
title = {Properties and numerical evaluation of the Rosenblatt distribution},
author = {Mark S. Veillette and Murad S. Taqqu},
journal= {arXiv preprint arXiv:1307.5990},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.3150/12-BEJ421 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)