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Title: The Maximum Likelihood Estimates of Multinomial Parameters Subject to Stochastic Order with Equality
Other Titles: 有等式隨機序的最大概似估計
Authors: 張少同
Shao-Tung Chang and Hsiao-Chuan Lu
Issue Date: Oct-1999
Publisher: 國立臺灣師範大學研究發展處
Office of Research and Development
Abstract: 長久以來,有關隨機序的估計問題一直被廣泛的討論與應用,然而在許多實際的應用上,我們發現兩組多項式分配的參數p和q除了隨機之外,可能還有其他的關係,例如相等、相差一個常數,或是成倍數關係。我們對參數了解愈多,愈能夠得到更精確的估計,因而在文章中,我們仿效Barlow及Brunk(1972)的方法推得在隨機序與部分等式條件下,多項式參數的最大概似估計。我們依單樣本和雙樣本分別討論並提供應用實例,此外我們也探討估計的一致性問題。
The problems of maximum likelihood estimates of multinomial parameters subject to stochastic ordering have been widely discussed. However, in some applications, the multinomial parameters p and q may not only satisfy the stochastically ordered constraints but also the equality of some of these parameters. We follow Barlow and Brunk's method (1972) and obtain the Fenchel duality projection-type maximum likelihood estimates of multinomial parameters under this modified hypothesis for both one-sample and two-sample problems. The consistency of the estimates is proved and. an example is also presented as an illustration.
Other Identifiers: E4688E89-BF04-5C7D-D13E-E80E7EC36F0A
Appears in Collections:師大學報:數理與科技類

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