論文提要

本文主要在探討各種分配函數之間關聯性，而討論的分配主要的計有二項、常態、……等三十種分配，而次要的分配加起來總共約有一百種之多。全文共分六章約十五萬餘言。首章為緒論，說明本人研究此一題目的動機、目的、方法以及所遭遇的限制等等，並將本文的架構以及各章節的安排情形作一簡單的說明。

第二章起至第五章止為本文的重心所在。首先于第二章內由次數曲線的觀點來探討各種分配函數之間的關係，接著于第三、第四及第五章中則分別探討離散、連續及抽樣分配函數之間的各種關聯性，最後則于第六章內作一結論並說明如何應用這些分配函數之間的關聯性以解決有關統計上的各種問題。

特別值得一提的是本文中定義了兩個新的分配函數—正弦分配及餘弦分配，有關其性質及與其他分配之間的關係在第四章之第八節詳述。此節亦是本文的研究重心之一。此外，本人亦於第六章結論之中定義了分配函數之間的”大小關係“使得各種分配函數在此一定義之下，吾人可以兩兩且較期間的大小關係，此亦為本文之新的嘗試，尚祈統計界的先進及前輩們多多指教。

參考書刊

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