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arXiv · 1307.5990

Properties and numerical evaluation of the Rosenblatt distribution

Mark S. Veillette·Murad S. Taqqu
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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 Lévy-Khintchine formula and derive asymptotic properties of the Lévy 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.

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Mark S. Veillette, Murad S. Taqqu. 2013-07-23. Properties and numerical evaluation of the Rosenblatt distribution. https://doi.org/10.3150/12-bej421

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