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A Note on a Paper of Barnes and Tucker
Author(s) -
Hall Peter
Publication year - 1979
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-19.1.170
Subject(s) - independent and identically distributed random variables , mathematics , random variable , combinatorics , constant (computer programming) , statistics , computer science , programming language
Let X 1 , X 2 , X 3 , … be independent and identically distributed random variables and let X nr denote the r 'th largest of { X 1 , X 2 , …, X n ), 1 ⩽ r ⩽ n . In a recent paper in this Journal, Barnes and Tucker examined conditions under which X n 1 / b ( n ) → c in probability or with probability one, where c and b ( n ), n ⩾ 1, are constants. In this note we continue their examination and study the convergence of X nr / b ( n ), r ⩾ 1, to c . We improve on Barnes and Tucker's results in the case r = 1.