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On distributions having the almost-lack-of-memory property

Part of:Distribution theorySpecial processes

Published online by Cambridge University Press:  14 July 2016

S. Chukova and
B. Dimitrov
S. Chukova*
Affiliation:
University of Sofia
B. Dimitrov*
Affiliation:
University of Sofia
*
∗ Postal address for both authors: Faculty of Mathematics and Information, University of Sofia, Sofia 1126, Anton Ivanov Str. 5, Bulgaria.
∗ Postal address for both authors: Faculty of Mathematics and Information, University of Sofia, Sofia 1126, Anton Ivanov Str. 5, Bulgaria.
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Abstract

It is shown that random variables X exist, not exponentially or geometrically distributed, such that

P{X – b ≧ x | X ≧ b} = P{X ≧ x}

for all x > 0 and infinitely many different values of b. A class of distributions having the given property is exhibited. We call them ALM distributions, since they almost have the lack-of-memory property. For a given subclass of these distributions some phenomena relating to service by an unreliable server are discussed.

Keywords

PROBABILITY DISTRIBUTIONSEXPONENTIAL (GEOMETRIC) DISTRIBUTIONUNRELIABLE SERVERBLOCKING TIMELACK-OF-MEMORY PROPERTY

MSC classification

Primary:62E15: Exact distribution theory
Secondary:60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 3 , September 1992, pp. 691 - 698
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research completed with the financial support of the Ministry of Science and Higher Education, under contract N 43–1987.

References

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