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Properties and numerical evaluation of the Rosenblatt distribution

Authors :
Veillette, Mark S.
Taqqu, Murad S.
Source :
Bernoulli 2013, Vol. 19, No. 3, 982-1005
Publication Year :
2013

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.<br />Comment: 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)

Subjects

Subjects :
Mathematics - Statistics Theory

Details

Database :
arXiv
Journal :
Bernoulli 2013, Vol. 19, No. 3, 982-1005
Publication Type :
Report
Accession number :
edsarx.1307.5990
Document Type :
Working Paper
Full Text :
https://doi.org/10.3150/12-BEJ421