Title: , X, , m1 m2 m2 m1 , m2 m1 m2 ,, m1 '
1?????? ??????? ???????
2?????? ???????
- ????? ?????? ??????? ??????? ??? ??? ???? ??
????????. - ????????? ????? ?????, ???? ??? ????? ????? ?????
???? ???? ???? ????? ????? ????
3????? ?????? ???????
???? ?????, X, ??? ????? ????, ???? ??? ??? m1
?- m2 (m2 gt m1 , m2 m1 ????? ???????? ??????)
?? ???? ???? ????? m2 ,, m1 ???? ???????.
????? ???? ????? ????? ????? ???? ????. ??????
???? ??? ???? ??????? 1/6. ????? ?? ???? ???????
?????? ???????? ??? 1/10. ????? ?? ???? ??????
?????? (0,1 ????) m10, m21 ????????? ??? ½.
4??? ?? ?????? ???????
- ???? ?????? ??????? ???? ???? ???????
?????-??????. - identical and independent distribution iid
- ?? ???? ???????? ????? ??? ????? ???? ?????
???? ????? ????? - ????? ?????? ???? ?????? ?????.
-
- ??? ?? ????? ??????? ???? ???? ?"? ???? ????? ??
???? ???? ???? ?? ??? ????? ?- 0 ???? ???? ?- 1.
??? ????? ????? ????
5- ???? ?????? ???????? ????? ?? ???? ?????? ?????
?????? ????, ???? ???? ?? ???? ????? ???????
????? - ?????? ?? ???? ??? ??? ????? ????? ????? ??????
??????? ?? ??? ????????, ????? ??????.
6??????
- ??? ??? ??????? ???????, ????? ??-???? ????
?????? ?? ????? ??? ???? ???? ???????? ???????
???????. - ??? ??? ????? ????? ?? ??????? ????? ??????
?????, ?? ???? ???? ?? ???? ???? ?? ????? ???.
7???? ??????
- ?? ?????? ?? ??????? ??? ???? ??? ????? ???.
- ???? ???? ????? ?? ?? ???? ????? ???? ?????,
???? ??????? ???? ??????. - ??? ???? ?? ?? ????? ???????? ??? ????? ????? ??
???? ?????? ?? ???? ????? ??????? ??????? ?? ??
??? ???? ???? ????. - ??? ?????? ????? ???? ??? ?????? ??????? ??????,
????? ??? ???? ?????? ???? ??????? ???? ????
????? ???????
8??? ?????? ?????? ????????
9Linear Congruential Method ???? ????? ???????
???? a, b, m ?? ??????? ?????? (???? a293,
b57,111, m65,536 ). ???? ??????? x0 ????
?????? (seed) ?? ????? ???? ????? ????.
?? ????? ???? ????? ??? 0 ?-1 ??? ???? ???? ?? Xj
?-m.
?????? ???? ?????? ??????? ???? ????? ???????
?????? ????? ?? ???? ????? ??? (??? ???? ??????
??? ???? ??????). ????? ?? ??? ?? ??????? ????
???? ?????? ?????? ??? ????.
10????? ????? ?????? ???????
?? ????? ?? ???? ???? ???? ?????? ???? ???? ?????
?? ?????. ???? ?? ?? ?????? ???? ????? ??????. ??
??? ???? ???? 16 ?????? ????? ?????.
11??? ??????
???? ?????? ?????? ?????? ????? ????? ?????? ???
m (???? ????? ???). ??? ???? ? m ???? ????
????. ??????? ???? ???? ???? ???? ?? 2 ??????
??? ?? ????.
12??? ???? ??????? ??????? ????? ????
- ???? ???? ??? ??? ????? ??? ?? ??? ?? ????????
?? ?????? ????? - ?? 4 ???? ?? ?? m, ?? 4 ???? ?? a-1
- ????? ???? ????? ????? ????? ?? b ?- m ??? 1
- ?? p ??? ???? ?????? ????? ?? m , ?? p ???? ??
a-1.
13????? ?????? X0 ?? ??? ??????
a 13 m 26 64 c 0
14????? ?? ?????? ???????
- ????? ????? ????? ???? ?? ?????? ?????? ????
?????? ?? ?????? ??????? ?????? ??? ??? ????
?????? ???????. - ?????? ????? ????? ????? ???? ?? ??? ???????? ???
????? ??????? ???? ???????? ????? ??? 0 ? 1. - ????? ????? ?? ???? ?????? ??????? ?? ??????,
???? ?????? ??????? ???????? ???? ??????
????????? ??????, ???????? ?? ???? ???????
???????? ???????. - ????????, ???? ?????? ??????? ????????, ?????
?????? ????? ????????, ??? ?????? ????? ????????
??????? ?? ?????? (?????? a, b ?-m ????? ??????
????????) ????? ????, ??? ????? ?? ?????? ???????
???.
15???? ???????
H0Ri U0,1 H1Ri U0,1
16???? ?????????? ???????
????? ?? ?????? ??? ???????? ???????? ??????? ??
???????? ??????
???? ???????? ???????? ??????? ?? ?????? ?????
??????? ??
17???? ?????????? ??????? - ????
???? ?????????? ??????? ????? ?? ??????
?????????? ?????????? ??? F(x) ???? SN(x)
???????? ???????? ?? D ????? (????? ?????? ?????
???? ???????? ?? SN(x) ????? ???? (F(x) ???? N
?????. ???? ???? ???? ?? ?????.
18????? ?????
??? 1 ????? ?????? ??????? ???? ?? ??????
??????? ???????? ???? ?? ??????? ????? ?????
????? ?????. ??? ????? ???? ???? ??? ? 1 ?? N
??? 2 ??? D D-
19????? ????? - ????
??? 3 ??? ?? D
??? 4 ???? ?????? ???? ???? ?????? ???????? ??
?????????? ??????? ??? ?? ???? ?????? ???? ???
???????? (???????) ????? ????? ?????.
??? 5 ??? ?? ????? ?? ?????? D ????? ???? ?????
?????? ??? ?? ????? ? 0 ????? ???????
???????? ?????.
20?????
21????? - ????
???? ????? ????? ??? 0.26 ???? ????? ????
? N5 ???? ?????? ??? 0.565 ????
?????? ?? ?????? ???????? ????? ???? ???????
?????.
22????
23???? ?? ?????? ??????? ??????? ???????
????? ????? ????? ??????? ???????. ??????? ????
?????? ?????? ??????? ??? 0 ? - 1
24????? ????
??? ????? ??????? ??????? ?????? F(x) ???? ?????
?? ????? ?????? ?????? R???????? ??????? ?? F(x)
25????? ??????? ???????
26????? 2 ???? ??????? ???????
27???? ?????? ?? ???????? ?????????
28??????? ?????? ?????
??????? ?????? ????? ???? ?????? ??????? ????
????? ?? ????? ???? ??? ??????? ????? ????. ???
????? ????? ???? ?????? (??????? ?? ????? ?????)
????? ??????. ?? ??? ?????? ???????? ???? ??????
??? ????? ??? ?????? ???????? ???? ??????.
????? ?? ????? ???? ?? ???? ?????? ?????? ??
?????? ???? 2.76 1.83 0.8 1.45 1.24
29????? ???????
30??????? ??????? ??????
1.0
0.8
0.6
0.4
0.2
0
1.0
2.0
3.0
31????? ???????? ???????
when