臺灣博碩士論文加值系統

由於pi有著良好的隨機性且已有大量位數,因此我們嘗試能否利用pi的隨機性製作新的亂數產生器.
我們先探討前人所作的亂數產生器(如LCG、MRG、MCG等).
以及統計測試亂數產生器的方法(如Chi Square Test、K-S Test、Runs Test等).
在本論文中,我們的產生數字的方法是在pi數列中以5個數字為一分割, 然後取{1,2,3,4,5}的隨機任意排列,
接著利用此排列產生介於0~99999的五位數隨機整數.
最後統計測試我們的亂數產生器產生的亂數,以評估我們設計的產生器之改良方向與發展潛力.

1 簡介 4
1.1 Rogers-Harrel-Wang演算法 5
2 常見的亂數產生器與統計實證檢定 8
2.1 線性同於產生器 9
2.2 多項遞迴產生器 10
2.3 矩陣同餘產生器 11
2.4 均勻分配檢定 14
2.4.1 Chi-square Test 14
2.4.2 Kolmogorov-Smirnov Test 15
2.5 隨機性檢定 17
2.5.1 Runs Test 17
2.5.2 Runs Above and Below Mean Test 18
3 pi序列隨機排列亂數產生器與統計測試分析 19
3.1 pi序列隨機排列亂數產生器 19
3.2 統計測試與分析 21
4 結論
A pi數列的前500個5位數 26

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