New results on stochastic comparison of order statistics from heterogeneous Weibull populations

Abstract Let X 1 , … , X n be independent random variables with X i ∼ W ( α , λ i ) , i = 1 , … , n . Let Y 1 , … , Y n be a random sample of size n from a Weibull distribution with common parameters α , λ . Let λ min denote the minimum of λ i , i = 1 , … , n . If λ ≥ ( ∏ i = 1 n λ i α ) 1 n λ min α − 1 , where α > 1 , it is shown that the largest order statistics X n : n is greater than the largest order statistics Y n : n according to the dispersive ordering.