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 [A<sub>1</sub>,B<sub>1</sub>]=[0,1] And [A<sub>n</sub>,B<sub>n</sub>] 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<sub>n</sub>,B<sub>n</sub>]; And choose [A<sub>n+1</sub>,B<sub>n+1</sub>] to be [C<sub>n</sub>,B<sub>n</sub>], [A<sub>n</sub>,D<sub>n</sub>] or [C<sub>n</sub>,D<sub>n</sub>] with probabilities p, q, r respectively such that p+q+r=1. Kennedy showed that the limiting distribution of [A<sub>n</sub>,B<sub>n</sub>] 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.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002003389 |
| Creators | 洪英超, Hung, Ying Chau |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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