Ӧ�ø���ͳ�� 2009, 25(4) 409-420 DOI:      ISSN: 1001-4268 CN: 31-1256

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Article by
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ժҪ�� ���ڼ򵥼��������Ŷȼ���,
Zhang (2002)�����һ���Ͻ��ͼ���.
ȡ��ͬ�IJ���$\lambda$�Ͳ�ͬ��Ȩ����$q(t)$,
������������Kolmogorov-Smirov����, Berk and Jones
(1979)��������е��Ͻ��ͼ���.
�����н��Լ�����$\lambda$��$q(t)$����Ӧ�ļ��������������µľ�ȷ�ֲ�.
Ȼ��, ��Բ�ͬ������, ``��''�ļ����Dz�ͬ��,
����б�Ҫ�����������$\lambda$��$q(t)$���, ���۸������.
���Ķ����������$\lambda$��$q(t)\equiv 1$���,
��������Ӧ�Ͻ��ͼ���ͳ������������µľ�ȷ�ֲ�. ����������$n$�ϴ�ʱ,
��ȷ�ֲ��ļ���ʱ��ϳ�, ���Ļ�ͨ��ģ��Ƚϵõ����ڲ�ͬ��������,
Ӧ���õļ��㷽��. ���, ����һ��ʵ�����Ӷ�ǰ���������Լ�˵��.
�ؼ����� ��ȷ�ֲ�   ����Dz���Ȼ��   ����Ŷȼ���.  
On Exact Distribution of a Class of Supremum-type\\Statistics for Goodness of Fit
Wei Bocheng:Li Guoying:Zhao Zhiyuan
College of Mathematical Sciences, Guangxi Normal University College of Applied Sciences, Beijing University of Technology Academy of Mathematics and System Sciences, Chinese Academy of Sciences
Abstract: For goodness of fit tests with simple null hypothesis,
Zhang (2002) constructed a classes of supremum-type tests. Different
parameter $\lambda$ and different weighted function $q(t)$ result in
different tests, including the Kolmogorov-Smirov test, Berk and
Jones (1979) test and so on. So far, only a few tests corresponding
to particular $\lambda$ and $q(t)$ have been studied in the
literature. However, for different problems, the ``best'' tests are
different. It is necessary to discuss the tests for all $\lambda$
and the general $q(t)$. In this paper, the exact distributions of
the test statistics for all $\lambda$ and $q(t)\equiv 1$ are
derived. When sample size $n$ is large, it takes a long time to get
the exact quantile. So we give some advice on the computation
methods for different sample size by simulation studies, and a real
example to simply illustrate the above methods.
Keywords: Exact distribution   generalized nonparametric likelihood ratio   goodness-of-fit test.  
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