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, X, , m1 m2 m2 m1 , m2 m1 m2 ,, m1 '

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????????? ????? ?????, ???? ??? ????? ????? ????? ???? ???? ???? ????? ????? ???? ... Linear Congruential Method. ???? ????? ??????? ... – PowerPoint PPT presentation

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Title: , X, , m1 m2 m2 m1 , m2 m1 m2 ,, m1 '


1
?????? ??????? ???????
2
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  • ????? ?????? ??????? ??????? ??? ??? ???? ??
    ????????.
  • ????????? ????? ?????, ???? ??? ????? ????? ?????
    ???? ???? ???? ????? ????? ????

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
???? ??????
  • ?? ?????? ?? ??????? ??? ???? ??? ????? ???.
  • ???? ???? ????? ?? ?? ???? ????? ???? ?????,
    ???? ??????? ???? ??????.
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  • ??? ?????? ????? ???? ??? ?????? ??????? ??????,
    ????? ??? ???? ?????? ???? ??????? ???? ????
    ????? ???????

8
??? ?????? ?????? ????????
9
Linear 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
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  • ????? ????? ????? ???? ?? ?????? ?????? ????
    ?????? ?? ?????? ??????? ?????? ??? ??? ????
    ?????? ???????.
  • ?????? ????? ????? ????? ???? ?? ??? ???????? ???
    ????? ??????? ???? ???????? ????? ??? 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
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21
????? - ????
???? ????? ????? ??? 0.26   ???? ????? ????
? N5 ???? ?????? ??? 0.565 ????
?????? ?? ?????? ???????? ????? ???? ???????
?????.
22
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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
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30
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1.0
0.8
0.6
0.4
0.2
0
1.0
2.0
3.0
31
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