The Annals of Probability

Exponential Life Functions with NBU Components

Moshe Shaked

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Abstract

Homogeneous nondecreasing functions of independent NBU random variables are studied. Two results of Block and Savits are improved. It is shown that if a coherent system, formed from independent NBU components, has exponential life then it is essentially a series system with exponential components. Also, it is shown that if a strictly increasing homogeneous function of independent NBU random variables has an exponential distribution then it is essentially a univariate function of one of its variables which must, then, be exponential. A new characterization of the MNBU class of distributions of Marshall and Shaked is derived, and a new proof of the closure of the class of NBU distributions under formation of nonnegative homogeneous increasing functions is given.

Article information

Source
Ann. Probab., Volume 11, Number 3 (1983), 752-759.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993519

Digital Object Identifier
doi:10.1214/aop/1176993519

Mathematical Reviews number (MathSciNet)
MR704561

Zentralblatt MATH identifier
0528.62081

JSTOR
links.jstor.org

Subjects
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62H05: Characterization and structure theory

Keywords
Homogeneous increasing functions coherent life functions multivariate NBU exponential distribution upper set

Citation

Shaked, Moshe. Exponential Life Functions with NBU Components. Ann. Probab. 11 (1983), no. 3, 752--759. doi:10.1214/aop/1176993519. https://projecteuclid.org/euclid.aop/1176993519


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