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The renewal-process stationary-excess operator

Published online by Cambridge University Press:  14 July 2016

Ward Whitt
Ward Whitt*
Affiliation:
AT&T Bell Laboratories
*
∗ Postal address: AT&T Bell Laboratories, HO 4M-326, Crawfords Corner Road, Holmdel NJ 07733, USA.
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Abstract

This paper describes the operator mapping a renewal-interval distribution into its associated stationary-excess distribution. This operator is monotone for some kinds of stochastic order, but not for the usual stochastic order determined by the expected value of all non-decreasing functions. Conditions for a renewal-interval distribution to be larger or smaller than its associated stationary-excess distribution for several kinds of stochastic order are determined in terms of familiar notions of ageing. Convergence results are also obtained for successive iterates of the operator, which supplement Harkness and Shantaram (1969), (1972) and van Beek and Braat (1973).

Keywords

RENEWAL THEORYSTATIONARY POINT PROCESSPALM THEORYSTOCHASTIC MONOTONICITYSTOCHASTIC ORDERMONOTONE LIKELIHOOD RATIOFAILURE RATEITERATED OVERSHOOT DISTRIBUTIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 156 - 167
Copyright
Copyright © Applied Probability Trust 1985 

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