On a class of perimeter-type distances of probability distributions
On a class of perimeter-type distances of probability distributions
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关于一类概率分布的周长型距离
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
F. Österreicher
中科院分区：
文献类型：
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作者：
F. Österreicher
本文研究的f-发散类If，p G（l，oo）推广了作者在[9]中提出并应用于[9]以及Reschenhofer和Bomze [11]在假设检验的不同领域中的f-发散。本文的主要结果确保了，对于每个p €（1，oo），相应的散度的平方根定义了概率分布集合上的距离。因此，它推广了Kafka、Osterreicher和Zerze在[6]中关于例4中对p = 2所作的有关陈述。从以前的文献对这个问题的最大权力/发散定义的距离是已知的后续类。对于给定的Hellinger-发散类（pu）= 1 + u -（u-u ~），sE（0，1），Csiszar和Fischer [3]已经证明了最大幂是min（s，1 - s）.对于以下两类，最大功率与它们的参数一致。根据f（a）（u）给出的类=| l - u，a €（0，1]，由Boekee [2]研究.前一个类和这个类都有特殊情况s = a =。这个著名的案例是由Matusita [8]。给出的类
The class If , p G ( l ,oo] , of /-divergences investigated in this paper generalizes an /-divergence introduced by the author in [9] and applied there and by Reschenhofer and Bomze [11] in different areas of hypotheses testing. The main result of the present paper ensures that, for every p € (1, oo), the square root of the corresponding divergence defines a distance on the set of probability distributions. Thus it generalizes the respecting statement for p = 2 made in connection with Example 4 by Kafka, Osterreicher and Vincze in [6]. From the former literature on the subject the maximal powers of /-divergences defining a distance are known for the subsequent classes. For the class of Hellinger-divergences given in terms of pu) = 1 + u — (u --u~) , s £ (0,1) , already Csiszar and Fischer [3] have shown that the maximal power is min(s, 1 — s). For the following two classes the maximal power coincides with their parameter. The class given in terms of f(a)(u) = | l — u , a € (0,1], was investigated by Boekee [2]. The previous class and this one have the special case s = a = in common. This famous case is attributed to Matusita [8]. The class given by