Abstract
It is shown that random variables X exist, not exponentially or geometrically distributed, such thatP{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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference7 articles.
1. 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.
2. A characteriszation of the geometric distribution related to random sums
3. Khalil Z. , Dimitrov B. and Petrov P. (1989) On the total execution time on an unreliable server with explicit breakdowns. Concordia University Technical Report.
Cited by
24 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Memory of Distributions: A Renewal Theoretic Approach;Journal of the Indian Society for Probability and Statistics;2022-04-08
2. Lack-of-partial-memory and aging properties of multivariate generalized Marshall-Olkin distributions;Communications in Statistics - Theory and Methods;2021-06-01
3. Distributions and Random Processes Related to Queueing and Reliability Models;Queueing Theory 2;2021-04-02
4. Bathtub Distributions;Reliability Modelling and Analysis in Discrete Time;2018
5. References;Reliability Modelling and Analysis in Discrete Time;2018