کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1150071 | 957911 | 2007 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Distribution of record statistics in a geometrically increasing population
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Distribution of record statistics in a geometrically increasing population Distribution of record statistics in a geometrically increasing population](/preview/png/1150071.png)
چکیده انگلیسی
The probability function and binomial moments of the number Nn of (upper) records up to time (index) n in a geometrically increasing population are obtained in terms of the signless q-Stirling numbers of the first kind, with q being the inverse of the proportion λ of the geometric progression. Further, a strong law of large numbers and a central limit theorem for the sequence of random variables Nn, n=1,2,â¦, are deduced. As a corollary the probability function of the time Tk of the kth record is also expressed in terms of the signless q-Stirling numbers of the first kind. The mean of Tk is obtained as a q-series with terms of alternating sign. Finally, the probability function of the inter-record time Wk=Tk-Tk-1 is obtained as a sum of a finite number of terms of q-numbers. The mean of Wk is expressed by a q-series. As k increases to infinity the distribution of Wk converges to a geometric distribution with failure probability q. Additional properties of the q-Stirling numbers of the first kind, which facilitate the present study, are derived.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 137, Issue 7, 1 July 2007, Pages 2214-2225
Journal: Journal of Statistical Planning and Inference - Volume 137, Issue 7, 1 July 2007, Pages 2214-2225
نویسندگان
Ch.A. Charalambides,