کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7547990 | 1489839 | 2018 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Random cyclic polygons from Dirichlet distributions and approximations of Ï
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آمار و احتمال
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چکیده انگلیسی
The classical Archimedean approximation of Ï uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R2. When n vertices are independently and uniformly randomly selected on the circle, a random inscribed or circumscribing polygon can be constructed and it is known that their semiperimeter and area both converge to Ï almost surely as nââ and their distributions are also asymptotically Gaussian. In this paper, we extend these results to the case of random cyclic polygons generated from symmetric Dirichlet distributions and show that as nââ, similar convergence results hold for the semiperimeters or areas of these random polygons. Additionally, we also present some extrapolation estimates with faster rates of convergence.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 140, September 2018, Pages 84-90
Journal: Statistics & Probability Letters - Volume 140, September 2018, Pages 84-90
نویسندگان
Shasha Wang, Wen-Qing Xu,