کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1150123 957913 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stochastic comparisons of order statistics in the scale model
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Stochastic comparisons of order statistics in the scale model
چکیده انگلیسی

Independent random variables Xλ1,…,XλnXλ1,…,Xλn are said to belong to the scale family of distributions if Xλi∼F(λix)Xλi∼F(λix), for i=1,…,n, where F is an absolutely continuous distribution function with hazard rate r   and reverse hazard rate r˜. We show that the hazard rate (reverse hazard rate) of a series (parallel) system consisting of components with lifetimes Xλ1,…,XλnXλ1,…,Xλn is Schur concave (convex) with respect to the vector λλ, if x2r′(x)x2r′(x)(x2r˜′(x)) is decreasing (increasing). We also show that if xr(x) is increasing in x  , then the survival function of the parallel system is increasing in the vector λλ with respect to p  -larger order, an order weaker than majorization. We prove that all these new results hold for the scaled generalized gamma family as well as the power-generalized Weibull family of distributions. We also show that in the case of generalized gamma and power generalized Weibull distribution, under some conditions on the shape parameters, the vector of order statistics corresponding to Xλi'sXλi's is stochastically increasing in the vector λλ with respect to majorization thus generalizing the main results in Sun and Zhang (2005) and Khaledi and Kochar (2006).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 141, Issue 1, January 2011, Pages 276–286
نویسندگان
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