Distributional Properties of Exceedance Statistics

Jacek Wesołowski , Mohammad Ahsanullah

Abstract

Behaviour of a sequence of independent identically distributed random variables with respect to a random threshold is investigated. Three statistics connected with exceeding the threshold are introduced, their exact and asymptotic distributions are derived. Also distribution-free properties, leading to some common and some new discrete distributions, are considered. Identification of equidistribution of observations and the threshold are discussed. In this context relations between the exponential and gamma distributions are studied and a new derivation of the celebrated Laplace expansion for the standard normal distribution function is given.
Author Jacek Wesołowski ZRPSM
Jacek Wesołowski,,
- Department of Probability and Mathematical Statistics
, Mohammad Ahsanullah
Mohammad Ahsanullah,,
-
Journal seriesAnnals of the Institute of Statistical Mathematics, ISSN 0020-3157, 1572-9052
Issue year1998
Vol50
No3
Pages543-565
Keywords in Englishapproximation discrete distribution, Characterization, distribution-free properties, Exceedance statistics, random threshold, standard normal distribution function, Statistics for Business/Economics/Mathematical Finance/Insurance, Statistics, general
DOIDOI:10.1023/A:1003533730137
URL http://link.springer.com/article/10.1023/A%3A1003533730137
Score (nominal)0
Citation count*24 (2015-04-09)
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