Report
Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables
| العنوان: | Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables |
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| المؤلفون: | Veillette, Mark S., Taqqu, Murad S. |
| سنة النشر: | 2010 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability, 60E05, 60E10, 60E99 |
| الوصف: | Consider the sum $Z = \sum_{n=1}^\infty \lambda_n (\eta_n - \mathbb{E}\eta_n)$, where $\eta_n$ are i.i.d.~gamma random variables with shape parameter $r > 0$, and the $\lambda_n$'s are predetermined weights. We study the asymptotic behavior of the tail $\sum_{n=M}^\infty \lambda_n (\eta_n - \mathbb{E}\eta_n)$ which is asymptotically normal under certain conditions. We derive a Berry-Essen bound and Edgeworth expansions for its distribution function. We illustrate the effectiveness of these expansions on an infinite sum of weighted chi-squared distributions. Comment: 19 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1010.3948 |
| رقم الانضمام: | edsarx.1010.3948 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |