Multivariate Distributions with Exponential Minimums
Loading...
Authors
Esary, James D.
Marshall, Albert W.
Subjects
Advisors
Date of Issue
1970-09
Date
Publisher
Monterey, California: Naval Postgraduate School
Language
Abstract
The multivariate distribution of a set of random variables has exponential minimums if the minimum over each subset of the variables has an exponential distribution. Such distributions are shown equivalent to the more strongly structured multivariate exponential distributions described by Marshall and Olkin in 1967 in the sense that a multivariate exponential distribution can be found that gives the same marginal distribution for each minimum. The basic application of the result is that in computing the reliability of a coherent system a joint distribution for the component life lengths with exponential minimums can be replaced by a multivariate exponential distribution. It follows that the life length of the system has an increasing hazard rate average distribution. Other applications include characterizations of multivariate exponential distributions and the derivation of a positive dependence condition for multivariate distributions with exponential minimums.
Type
Technical Report
Description
This document has been approved for public release and sale; its distribution is unlimited.
Series/Report No
Department
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
NPS55EY7OO91A
Sponsors
Funding
Format
35 p.
Citation
Distribution Statement
Rights
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.