Report
Properties and numerical evaluation of the Rosenblatt distribution
| العنوان: | Properties and numerical evaluation of the Rosenblatt distribution |
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| المؤلفون: | Veillette, Mark S., Taqqu, Murad S. |
| المصدر: | Bernoulli 2013, Vol. 19, No. 3, 982-1005 |
| سنة النشر: | 2013 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory |
| الوصف: | 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. 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) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3150/12-BEJ421 |
| URL الوصول: | http://arxiv.org/abs/1307.5990 |
| رقم الانضمام: | edsarx.1307.5990 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.3150/12-BEJ421 |
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