張少同呂小娟Shao-Tung Chang and Hsiao-Chuan Lu2014-10-272014-10-271999-10-??http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/17795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.多項式參數最大概似估計隨機序最小平方投影Multinomial parametersMaximum likelihood estimateStochastic orderingLeast square projection