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On sequences of expected maxima and expected ranges

Part of: Distribution theory - Probability Nonparametric inference Integral transforms, operational calculus

Published online by Cambridge University Press:  30 November 2017

Nickos Papadatos
Nickos Papadatos*
Affiliation:
National and Kapodistrian University of Athens
*
* Postal address: Department of Mathematics, Section of Statistics and Operations Research, National and Kapodistrian University of Athens, Panepistemiopolis, 157 84 Athens, Greece. Email address: npapadat@math.uoa.gr
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Abstract

We investigate conditions in order to decide whether a given sequence of real numbers represents expected maxima or expected ranges. The main result provides a novel necessary and sufficient condition, relating an expected maxima sequence to a translation of a Bernstein function through its Lévy–Khintchine representation.

Keywords

Expected maximaexpected rangeBernstein functionLévy–Khintchine representationorder statistics

MSC classification

Primary: 62G30: Order statistics; empirical distribution functions 60E05: Distributions
Secondary: 44A60: Moment problems
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 4 , December 2017 , pp. 1144 - 1166
Copyright
Copyright © Applied Probability Trust 2017 

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