The Annals of Probability
- Ann. Probab.
- Volume 11, Number 3 (1983), 752-759.
Exponential Life Functions with NBU Components
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.
Ann. Probab., Volume 11, Number 3 (1983), 752-759.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62H05: Characterization and structure theory
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