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Switching Order Statistics through Random Power Contractions
Author(s) -
WesoŁowski Jacek,
Ahsanullah Mohammad
Publication year - 2004
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.2004.00330.x
Subject(s) - mathematics , order statistic , exponential distribution , exponential function , convolution random number generator , contraction (grammar) , exponential growth , statistics , power law , probability integral transform , statistical physics , random variable , mathematical analysis , random variate , marginal distribution , medicine , physics
Summary This paper investigates a new random contraction scheme which complements the length‐biasing and convolution contraction schemes considered in the literature. A random power contraction is used with order statistics, leading to new and elegant characterizations of the power distribution. In view of Rossberg's counter‐example of a non‐exponential law with exponentially distributed spacings of order statistics, possibly the most appealing consequence of the result is a characterization of the exponential distribution via an independent exponential shift of order statistics.