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- W2018762455 abstract "Abstract Let X 1 , … , X n be independent random variables with X i ∼ W ( α , λ i ) , where W ( α , λ i ) denotes a Weibull distribution with shape parameter α and scale parameter λ i , i = 1 , … , n . Let Y 1 , … , Y n be a random sample of size n from a Weibull distribution with shape parameter α and a common scale parameter λ . Firstly, we prove that the smallest order statistic X 1 : n is greater than the smallest order statistic Y 1 : n according to the convex transform order. Secondly, we prove that λ ≥ ( 1 n ∑ i = 1 n λ i α ) 1 α implies Y 1 : n ≤ disp X 1 : n ; and λ = ( ∏ i = 1 n λ i ) 1 n implies X 1 : n ≤ r h Y 1 : n . Let X 1 ∗ , … , X n ∗ be independent random variables with X i ∗ ∼ W ( α , λ i ∗ ) , i = 1 , … , n . Then ( λ 1 ∗ , … , λ n ∗ ) ≤ m ( λ 1 , … , λ n ) implies that X 1 : n ≤ r h X 1 : n ∗ for α > 1 and X 1 : n ∗ ≤ r h X 1 : n for 0 α ≤ 1 ." @default.
- W2018762455 created "2016-06-24" @default.
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- W2018762455 date "2013-07-01" @default.
- W2018762455 modified "2023-09-24" @default.
- W2018762455 title "Stochastic comparisons of series systems with heterogeneous Weibull components" @default.
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- W2018762455 doi "https://doi.org/10.1016/j.spl.2013.03.012" @default.
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