Publication:
Multivariate geometric distributions generated by a cumulative damage process

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Authors
Esary, James Daniel
Marshall, A. W.
Subjects
Advisors
Date of Issue
1973-03
Date
1973-03
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
Two (narrow and wide) multivariate geometric analogues of the Marshall-Olkin multivariate exponetial distribution are derived from the following cumulative damage model. A set of devices is exposed to a common damage process. Damage occurs in discrete cycles. On each cycle the amount of damage is an independent observation on a nonnegative random variable. Damages accumulate additively. Each device has its own random breaking threshold. A device fails when the accumulated damage exceeds its threshold. Thresholds are independent of damages, and have a Marshall-Olkin multivariate exponential distribution. The joint distribution of the random numbers of cycles up to and including failure of the devices has the wide multivariate geometric distribution. It has the narrow multivariate geometric distribution if the damage variable is infinitely divisible. (Author)
Type
Technical Report
Description
Series/Report No
Department
Identifiers
NPS Report Number
NPS55EY73041A
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Funder
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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