کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1148130 957821 2010 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Competition between discrete random variables, with applications to occupancy problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Competition between discrete random variables, with applications to occupancy problems
چکیده انگلیسی

Consider n   players whose “scores” are independent and identically distributed values {Xi}i=1n from some discrete distribution F. We pay special attention to the cases where (i) F   is geometric with parameter p→0p→0 and (ii) F   is uniform on {1,2,…,N}{1,2,…,N}; the latter case clearly corresponds to the classical occupancy problem. The quantities of interest to us are, first, the U-statistic W which counts the number of “ties” between pairs i, j; second, the univariate statistic Yr, which counts the number of strict r  -way ties between contestants, i.e., episodes of the form Xi1=Xi2=⋯=XirXi1=Xi2=⋯=Xir; Xj≠Xi1;j≠i1,i2,…,irXj≠Xi1;j≠i1,i2,…,ir; and, last but not least, the multivariate vector ZAB=(YA, YA+1,…,YB). We provide Poisson approximations for the distributions of W, Yr and ZAB under some general conditions. New results on the joint distribution of cell counts in the occupancy problem are derived as a corollary.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 140, Issue 8, August 2010, Pages 2204–2212
نویسندگان
, , ,