Coupon collector's problems with statistical applications to rankings
Coupon collector's problems with statistical applications to rankings
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优惠券收集者在统计应用排名方面遇到的问题
DOI：
10.1007/s10463-012-0382-9
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发表时间：
2013
影响因子：
1
通讯作者：
K.
中科院分区：
文献类型：
--
作者：
Aki;S. and Hirano;K.
基于广义Pólya瓮抽样，给出了优惠券回收者等待时间问题的一些新的精确分布。特别是，通常的波利亚瓮采样产生一个可交换的随机序列。在这种情况下，分布的另一种推导也可以从de Finetti定理得到。在具有多种优惠券的优惠券收集者的等待时间问题中，观察到的多种优惠券的顺序唯一地对应于一个字母排列。利用优惠券收集者问题的性质，提出了一种分析排序数据的字母排列群统计模型。在模型中，由于参数表示各种优惠券的比例，因此可以直观地理解观察到的排序。文中还给出了一些统计推断的例子。
Some new exact distributions on coupon collector’s waiting time problems are given based on a generalized Pólya urn sampling. In particular, usual Pólya urn sampling generates an exchangeable random sequence. In this case, an alternative derivation of the distribution is also obtained from de Finetti’s theorem. In coupon collector’s waiting time problems withkinds of coupons, the observed order ofkinds of coupons corresponds to a permutation ofletters uniquely. Using the property of coupon collector’s problems, a statistical model on the permutation group ofletters is proposed for analyzing ranked data. In the model, as the parameters mean the proportion of thekinds of coupons, the observed ranking can be intuitively understood. Some examples of statistical inference are also given.