Weibull distribution: Some stochastic comparisons results Article

Khaledi, BE, Kochar, S. (2006). Weibull distribution: Some stochastic comparisons results . JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 136(9), 3121-3129. 10.1016/j.jspi.2004.12.013

cited authors

  • Khaledi, BE; Kochar, S

authors

abstract

  • Let X1, ..., Xn be independent random variables such that Xi has Weibull distribution with shape parameter α and scale parameter λi, i = 1, ..., n. Let X1*, ..., Xn * be another set of independent Weibull random variables with the same common shape parameter α, but with scale parameters as λ * = ( λ1*, ..., λn * ). Suppose that λ over({succeeds or equal to}, m) λ *. We prove that when 0 < α < 1, ( X ( 1 ), ..., X( n ) ) over({succeeds or equal to}, st) ( X( 1 )*, ..., X( n )* ) . For α {greater than or slanted equal to} 1, we prove that X( 1 ) {less-than or slanted equal to}hr X( 1 ) *, whereas the inequality is reversed when α {less-than or slanted equal to} 1. Let Y1, ..., Yn be a random sample of size n from a Weibull distribution with shape parameter α and scale parameter over(λ, ̃) = ( ∏ i = 1n λi )1 / n, the geometric mean of the λi's. It is shown that X( n ) {greater than or slanted equal to}hr Y( n ) for all values of α and in case α {less-than or slanted equal to} 1, we also have that X( n ) is greater than Y( n ) according to dispersive ordering. In the process, we also prove some new results on stochastic comparisons of order statistics for the proportional hazards family. © 2005 Elsevier B.V. All rights reserved.

publication date

  • September 1, 2006

published in

Digital Object Identifier (DOI)

start page

  • 3121

end page

  • 3129

volume

  • 136

issue

  • 9