A characterization of the geometric distribution

1974 ◽  
Vol 11 (3) ◽  
pp. 609-611 ◽  
Author(s):  
A. C. Dallas
Keyword(s):  
Geometric Distribution ◽  
Conditional Variance ◽  
Memory Property ◽  
Lack Of Memory Property

The geometric distribution is characterized. The lack of memory property is replaced by the constancy of the conditional variance. Then the characterization is obtained.

A characterization of the geometric distribution

1974 ◽  
Vol 11 (03) ◽  
pp. 609-611
Author(s):  
A. C. Dallas
Keyword(s):  
Geometric Distribution ◽  
Conditional Variance ◽  
Memory Property ◽  
Lack Of Memory Property

The geometric distribution is characterized. The lack of memory property is replaced by the constancy of the conditional variance. Then the characterization is obtained.

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.

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.

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