Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T12:41:33.904Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Part of: Distribution theory Special 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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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

References

[1] Azlarov, T. and Volodin, N. (1986) Characterization Problems Associated with the Exponential Distribution. Springer-Verlag, Berlin.Google Scholar
[2] Dimitrov, B. and Khalil, Z. (1990) On a new characterization of the exponential distribution related to a queueing system with an unreliable server. J. Appl. Prob. 27, 221–226.Google Scholar
[3] Feller, W. (1966) An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley, New York.Google Scholar
[4] Jaiswal, N. K. (1968) Priority Queues. Academic Press, New York.Google Scholar
[5] Khalil, Z., Dimitrov, B. and Dion, J.-P. (1991) A characterization of the geometric distribution related to random sums. Comm. Statist. Stoch. Models. 7, 321–326.CrossRefGoogle Scholar
[6] Khalil, Z., Dimitrov, B. and Petrov, P. (1989) On the total execution time on an unreliable server with explicit breakdowns. Concordia University Technical Report.Google Scholar
[7] Khalil, Z. and Dimitrov, B. (1990) Some characterizations of the exponential distribution based on the service time properties of an unreliable server. Submitted to J. Appl. Prob.Google Scholar