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Limiting distributions of Kolmogorov‐Lévy‐type statistics under the alternative

 

作者: Andrzej Kozek,  

 

期刊: Canadian Journal of Statistics  （WILEY Available online 1987）
卷期: Volume 15, issue 1  

页码: 77-85

 

ISSN:0319-5724

 

年代: 1987

 

DOI:10.2307/3314864

 

出版商: Wiley‐Blackwell

 

关键词: Asymptotic distribution;empirical distribution function;Kolmogorov‐Smirnov metric;Prohorov‐Lévy metric

 

数据来源: WILEY

 

摘要:

AbstractLetXi, 1 ≤i≤n, be independent identically distributed random variables with a common distribution functionF, and letGbe a smooth distribution function. We derive the limit distribution of□{ρα(Fn, G) ‐α(F, G)}, whereFnis the empirical distribution function based onX1,…,Xnandαis a Kolmogorov‐Lévy‐type metric between distribution functions. For α ≤ 0 and two distribution functionsFandGthe metric pαis given by pα(F, G) = inf {ϵ ≤ 0:G(x‐ αϵ)

 

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