Stochastic Order Relations Among Parallel Systems from Weibull Distributions
Nuria Torrado,Subhash C. Kochar +1 more
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In this article, the effect of changes in the scale parameters (λ 1, λ 2, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings was investigated.Abstract:
Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.read more
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References
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TL;DR: In this paper, it was shown that the reverse hazard rate of Xn:n is Schur convex in λ, which is the same as the Schur-convexity of the survival function.
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Some new results on stochastic comparisons of parallel systems
TL;DR: In this article, it was shown that the hazard rate of a random sample of size n from an exponential distribution with common hazard rate λ ˜ = ( ni = 1 λ i ) 1 /n, the geometric mean of the λ I s s is greater than that of an independent exponential random variable X n : n.