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The rate of convergence in law of the maximum of an exponential sample
Author(s) -
Hall W. J.,
Wellner Jon A.
Publication year - 1979
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1979.tb00671.x
Subject(s) - mathematics , statistic , rate of convergence , exponential distribution , exponential function , order statistic , distribution (mathematics) , statistics , convergence (economics) , sample (material) , exponential family , mathematical analysis , physics , thermodynamics , electrical engineering , engineering , channel (broadcasting) , economics , economic growth
Summary We derive a uniform rate of convergence of (1– n ‐1 x) n to e ‐x (x < 0). It provides a uniform rate of convergence for the distribution of the largest order statistic in a sample from an exponential distribution to the “double exponential” extreme value distribution. It likewise provides a rate of convergence for the distribution of the smallest order statistic from a uniform distribution.