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

Stefanka Chukova; Boyan Dimitrov

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

Stefanka Chukova, Boyan Dimitrov

Kettering University

Research output: Contribution to journal › Article › peer-review

Abstract

It is shown that random variables X exist, not exponentially or geometrically distributed, such that P{X - b greater-than-or-equal-to x \ X greater-than-or-equal-to b} = P{X greater-than-or-equal-to 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.

Original language	American English
Journal	Journal of Applied Probability
Volume	29
State	Published - Sep 1 1992

Disciplines

Mathematics

Cite this

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title = "On distributions having the almost-lack-of-memory property",

abstract = " It is shown that random variables X exist, not exponentially or geometrically distributed, such that P{X - b greater-than-or-equal-to x \ X greater-than-or-equal-to b} = P{X greater-than-or-equal-to 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. ",

author = "Stefanka Chukova and Boyan Dimitrov",

note = "Journal of Applied Probability It is shown that random variables X exist, not exponentially or geometrically distributed, such that 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.",

year = "1992",

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language = "American English",

volume = "29",

journal = "Journal of Applied Probability",

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T1 - On distributions having the almost-lack-of-memory property

AU - Chukova, Stefanka

AU - Dimitrov, Boyan

N1 - Journal of Applied Probability It is shown that random variables X exist, not exponentially or geometrically distributed, such that 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.

PY - 1992/9/1

Y1 - 1992/9/1

N2 - It is shown that random variables X exist, not exponentially or geometrically distributed, such that P{X - b greater-than-or-equal-to x \ X greater-than-or-equal-to b} = P{X greater-than-or-equal-to 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.

AB - It is shown that random variables X exist, not exponentially or geometrically distributed, such that P{X - b greater-than-or-equal-to x \ X greater-than-or-equal-to b} = P{X greater-than-or-equal-to 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.

UR - https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-distributions-having-the-almostlackofmemory-property/86F7E7602296C2C28F802BDE267C7F44

M3 - Article

VL - 29

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -

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

Abstract

Disciplines

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Cite this