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Properties and numerical evaluation of the Rosenblatt distribution
- 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 :
- Mathematics - Statistics Theory
Subjects
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