Characterization of probability distributions similar to the exponential

Stefanka Chukova; Boyan N. Dimitrov; Zohel Khalil

doi:10.2307/3315752

Characterization of probability distributions similar to the exponential

Stefanka Chukova, Boyan N. Dimitrov, Zohel Khalil

Kettering University

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

Abstract

<p> A concept of the lack&hyphen;of&hyphen;memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost&hyphen;lack&hyphen;of&hyphen;memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.</p>

Original language	American English
Journal	The Canadian Journal of Statistics
Volume	21
DOIs	https://doi.org/10.2307/3315752
State	Published - Sep 1 1993

Keywords

Characterization theorems
almost‐lack‐of‐memory property
blocking time on unreliable server

Disciplines

Mathematics

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10.2307/3315752License: CC BY

https://onlinelibrary.wiley.com/doi/abs/10.2307/3315752

Cite this

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author = "Stefanka Chukova and Dimitrov, {Boyan N.} and Zohel Khalil",

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doi = "10.2307/3315752",

language = "American English",

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T1 - Characterization of probability distributions similar to the exponential

AU - Chukova, Stefanka

AU - Dimitrov, Boyan N.

AU - Khalil, Zohel

PY - 1993/9/1

Y1 - 1993/9/1

N2 - A concept of the lack&hyphen;of&hyphen;memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost&hyphen;lack&hyphen;of&hyphen;memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.

AB - A concept of the lack&hyphen;of&hyphen;memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost&hyphen;lack&hyphen;of&hyphen;memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.

KW - Characterization theorems

KW - almost‐lack‐of‐memory property

KW - blocking time on unreliable server

UR - https://digitalcommons.kettering.edu/mathematics_facultypubs/24

UR - https://onlinelibrary.wiley.com/doi/abs/10.2307/3315752

U2 - 10.2307/3315752

DO - 10.2307/3315752

M3 - Article

VL - 21

JO - The Canadian Journal of Statistics

JF - The Canadian Journal of Statistics

ER -

Characterization of probability distributions similar to the exponential

Abstract

Keywords

Disciplines

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