%0 Journal Article
%T Properties and numerical evaluation of the Rosenblatt distribution
%A Mark S. Veillette
%A Murad S. Taqqu
%J Statistics
%D 2013
%I arXiv
%R 10.3150/12-BEJ421
%X 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.
%U http://arxiv.org/abs/1307.5990v1