Open Access
August, 1983 Exponential Life Functions with NBU Components
Moshe Shaked
Ann. Probab. 11(3): 752-759 (August, 1983). DOI: 10.1214/aop/1176993519


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.


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Moshe Shaked. "Exponential Life Functions with NBU Components." Ann. Probab. 11 (3) 752 - 759, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0528.62081
MathSciNet: MR704561
Digital Object Identifier: 10.1214/aop/1176993519

Primary: 62N05
Secondary: 62H05

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

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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