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Convolution of the IFRA scaled-mins class. (English) Zbl 0619.60086

A nonnegative random variable is said to be IFRA (increasing failure rate average) if \(P\{T>\alpha t\}\geq [P\{T>t\}]^{\alpha}\) for all \(t\geq 0\) and \(0\leq \alpha <1\). A nonnegative random vector \(T=(T_ 1,...,T_ n)\) is said to belong to the IFRA scaled-mins class if \(\min_{1\leq i\leq n}a_ iT_ i\) is IFRA for all choices \(0<a_ i\leq \infty\), \(i=1,2,...,n.\)
In the paper it is shown that the IFRA scaled-mins class is closed under convolution. It is also shown that T belongs to the IFRA scaled-mins class if and only if E[H(T)\(\}\leq E^{1/\alpha}[H^{\alpha}(T/\alpha)]\) for all \(0<\alpha <1\) and all distribution functions H.
Reviewer: M.Shaked

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
62N05 Reliability and life testing
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