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

1992 ◽  
Vol 29 (3) ◽  
pp. 691-698 ◽  
Author(s):  
S. Chukova ◽  
B. Dimitrov
Keyword(s):  
Random Variables ◽  
Unreliable Server ◽  
Memory Property ◽  
The Given ◽  
Lack Of Memory Property

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.

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

1992 ◽  
Vol 29 (03) ◽  
pp. 691-698 ◽  
Author(s):  
S. Chukova ◽  
B. Dimitrov
Keyword(s):  
Random Variables ◽  
Unreliable Server ◽  
Memory Property ◽  
The Given ◽  
Lack Of Memory Property

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.

scholarly journals On revelation transforms that characterize probability distributions

1993 ◽  
Vol 6 (4) ◽  
pp. 345-357 ◽  
Author(s):  
S. Chukova ◽  
B. Dimitrov ◽  
J.-P. Dion
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Memory Property ◽  
Lack Of Memory Property

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the “revelation transform of probability distributions” and “relevation of random variables” is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified.

An unreliable server characterization of the exponential distribution

1994 ◽  
Vol 31 (1) ◽  
pp. 274-279 ◽  
Author(s):  
Janos Galambos ◽  
Charles Hagwood
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Service Time ◽  
Unreliable Server ◽  
Memory Property ◽  
Lack Of Memory Property

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.

An unreliable server characterization of the exponential distribution

1994 ◽  
Vol 31 (01) ◽  
pp. 274-279 ◽  
Author(s):  
Janos Galambos ◽  
Charles Hagwood
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Service Time ◽  
Unreliable Server ◽  
Memory Property ◽  
Lack Of Memory Property

Consider a workstation with one server, performing jobs with a service time, Y, having distribution function, G(t). Assume that the station is unreliable, in that it occasionally breaks down. The station is instantaneously repaired, and the server restarts the uncompleted job from the beginning. Let T denote the time it takes to complete each job. If G(t) is exponential with parameter A, then because of the lack-of-memory property of the exponential, P (T > t) = Ḡ(t) =exp(−γt), irrespective of when and how the failures occur. This property also characterizes the exponential distribution.

Characterizations of the Exponential Distribution via the Blocking Time in a Queueing System with an Unreliable Server

1998 ◽  
Vol 35 (1) ◽  
pp. 236-239 ◽  
Author(s):  
Jian-Lun Xu
Keyword(s):  
Exponential Distribution ◽  
Service Time ◽  
Coefficient Of Variation ◽  
Queueing System ◽  
Random Variables ◽  
Unreliable Server ◽  
Failure Times ◽  
Server Failure

The characterization of the exponential distribution via the coefficient of the variation of the blocking time in a queueing system with an unreliable server, as given by Lin (1993), is improved by substantially weakening the conditions. Based on the coefficient of variation of certain random variables, including the blocking time, the normal service time and the minimum of the normal service and the server failure times, two new characterizations of the exponential distribution are obtained.

scholarly journals A Stone-Weierstrass theorem for random functions

1970 ◽  
Vol 2 (2) ◽  
pp. 233-236 ◽  
Author(s):  
A. Mukherjea
Keyword(s):  
Random Function ◽  
Random Variables ◽  
Compact Set ◽  
Mean Square ◽  
Weierstrass Theorem ◽  
Random Functions ◽  
The Given ◽  
Uniformly Bounded

It is shown in this note that if Q is an algebra of uniformly bounded mean-square continuous real-valued random functions indexed in a compact set T, containing all bounded random variables and separating points of T (i.e., given t1 and t2 in T, there is a random function Xt in Q such that , then given any mean square continuous random function, there is a sequence in Q converging in mean square to the given random function uniformly on T.

scholarly journals Sibuya-type bivariate lack of memory property

2015 ◽  
Vol 134 ◽  
pp. 119-128 ◽  
Author(s):  
Jayme Pinto ◽  
Nikolai Kolev
Keyword(s):  
Memory Property ◽  
Lack Of Memory Property
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