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NUMBERS OF OBSERVATIONS NEAR ORDER STATISTICS
Author(s) -
Pakes Anthony G.
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2009.00551.x
Subject(s) - mathematics , order statistic , poisson distribution , statistic , mathematical proof , neighbourhood (mathematics) , statistics , sample (material) , mathematical analysis , geometry , chemistry , chromatography
Summary Limit theorems are obtained for the numbers of observations in a random sample that fall within a left‐hand or right‐hand neighbourhood of the k th order statistic. The index k can be fixed, or tend to infinity as the sample size increases unboundedly. In essence, the proofs are applications of the classical Poisson and De Moivre–Laplace theorems.