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Algebraic boundedness of sample statistics
Author(s) -
Kirby W.
Publication year - 1974
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr010i002p00220
Subject(s) - statistics , mathematics , skew , sample size determination , sample (material) , coefficient of variation , population , range (aeronautics) , order statistic , algebraic number , mathematical analysis , physics , demography , materials science , thermodynamics , sociology , astronomy , composite material
Some puzzling results from a computer simulation study are explained by showing that the sample skew coefficient has population‐independent bounds depending only on the sample size. Similar results are obtained for the coefficient of variation of positive data, the maximum standardized deviate, and the standardized range. The upper bounds of these statistics are ( n − 2)/( n − 1) 1/2 , ( n − 1) 1/2 , ( n − 1) 1/2 , and (2n) 1/2 .