کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6418086 | 1339320 | 2015 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the norming constants for normal maxima
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
Given n independent standard normal random variables, it is well known that their maxima Mn can be normalized such that their distribution converges to the Gumbel law. In a remarkable study, Hall proved that the Kolmogorov distance dn between the normalized Mn and its associated limit distribution is less than 3/logâ¡n. In the present study, we propose a different set of norming constants that allow this upper bound to be decreased with dnâ¤C(m)/logâ¡n for nâ¥mâ¥5. Furthermore, the function C(m) is computed explicitly, which satisfies C(m)â¤1 and limmâââ¡C(m)=1/3. As a consequence, some new and effective norming constants are provided using the asymptotic expansion of a Lambert W type function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 422, Issue 1, 1 February 2015, Pages 376-396
Journal: Journal of Mathematical Analysis and Applications - Volume 422, Issue 1, 1 February 2015, Pages 376-396
نویسندگان
Armengol Gasull, Maria Jolis, Frederic Utzet,