在眾多產生貝他分配的方法中，我們研究Kennedy的演算法。在本文中，我們探討在小樣本下，不同參數組合(k,p,q,r) 產生同一貝他分配的情形。 / There are mAny methods for generating a beta distribution. In this study, we focus on the method proposed by Kennedy (1988). Let [A₁,B₁]=[0,1] And [A_n,B_n] be rAndom subinterval of [0,1] defined recursively as follows. Take C , D to be the minimum And maximum of k i.i.d rAndom points uniformly distributed on [A_n,B_n]; And choose [A_n+1,B_n+1] to be [C_n,B_n], [A_n,D_n] or [C_n,D_n] with probabilities p, q, r respectively such that p+q+r=1. Kennedy showed that the limiting distribution of [A_n,B_n] has a beta distribution on [0,1] with parameters k(p+r) And k(q+r). 　　Based upon the known asymptotic result, we study the small-sample behaviors among those combinations of k, p, q, r that have the same Beta(m, n) distribution, where m = k(p+r), n = k(q+r), through simulations. We conclude that smaller k's basically have better performAnces.

本論文主要是介紹並評估一個R的軟體套件叫做"rBeta2009"。此套件是由Cheng et al. (2012) [8] 所設計，其目的是用來產生貝他分配(Beta Distribution)及狄氏分配(Dirichlet Distribution)的亂數。本論文特別針對此套件之(i)有效性(effiniency)、(ii)精確性(accuracy)及(iii)隨機性(randomness)進行評估，並與現有的R套件作比較。此外，本論文也介紹如何應用此套件來產生(i)反貝他分配(Inverted Beta Distribution)、(ii)反狄氏分配(Inverted Dirichlet Distribution)、(iii)Liouville分配及(iv)凸面區域上的均勻分配之亂數。 / A package in R called "rBeta2009", originally designed by Cheng et al. (2012) [6], was introduced and evaluated in this thesis. The purpose of the package is generating beta random numbers and Dirichlet random vectors. In this paper, we not only evaluated (i) the efficiency, (ii) the accuracy and (iii) the randomness, but also compare it with other R packages currently in use. In addition, it was also scrutinized in this thesis how to generate (i) inverted beta random numbers, (ii) inverted Dirichlet random vectors, (iii) Liouville random vectors, and (iv) uniform random vectors over convex polyhedron by using the same package.