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1	多變量d轉換的一些應用 / Some applications of multivariate d-transformations 郭錕霖 Unknown Date (has links) Jiang (1997) 首先提出多變量d轉換與其性質。利用多變量d轉換，我們可以定義新式的特徵函數，並且稱它們是多變量d特徵函數。在這篇論文中，我們將使用多變量d特徵函數來證明在普通的條件下，Dirichlet隨機向量的線性組合會分配收斂（converge in distribution）到一個對稱的分配。此外，當給定一個分配函數的多變量d特徵函數，我們將建構一個方法來決定此分配函數。另一方面，我們將證明多變量d特徵函數擁有很多類似傳統的特徵函數的性質。 / A multivariate d-transformation and its properties were first given by Jiang (1997). By means of the multivariate d-transformations, we can define new kinds of characteristic functions and call them multivariate d-characteristic functions. In this thesis, we will use the multivariate d-characteristic function to show that the linear combinations of Dirichlet random vectors, under regularity conditions, converge in distribution to a spherical distribution. Moreover, We will construct a method for constructing the distribution function with a given multivariate d-characteristic function. In addition, we will show that the multivariate d-characteristic function has many properties which are similar to those of the traditional characteristic function. 多變量d轉換多變量d特徵函數 Dirichlet分配對稱分配極限分配反演過程 multivariate d-transformation multivariate d-characteristic function Dirichlet distribution spherical distribution limiting distribution inversion process Carlson R

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多變量d轉換的一些應用 / Some applications of multivariate d-transformations