1、 l : 1996-12-16; : 1997-05-09 sZE 宫null 野 (v v , 116024) Knull1null LC s ZE,iZET 1 , V L=5b 1oMnull snullZEnullr q ms |null O211. 3null O212. 2 0null s ad9a9 ,+YMonte CarloZE9 KnaK1sBb ZEz,YYs, null2saTsr qbN, LC s ZE,iZET 1 , L=5b y M Y sN( a, null2),5X = ( Y- a)/ null S sN(0,1)byN,/ ) S sZEb 1null
2、 ZE snull 3null5null,1 |xSBK uW:x null - a, a,a |l3 ? Q s b/ E mb S= nullnull2 =Xf S (+) exp(- S2/ 2)? (-) - a+ 2anull1 sFZE Uim null1, null2# null,nulli 0, 1 uW ( s b Er qnull= 2null/(2null) b |a= 3,5null= 0null417 8; |a= 5,5null= 0null250 7br q yX |S =vBs$ b %B5, (0 5)s Uim+ ,ssY0null5,1,1null5,2,
3、35,itf * (x)T 0bA , 0 = ,11v =gr q1, / FZEb 2nullFZE n5 sf * (x)= exp(- x2/2)f * (x)= null n pnf *n (x) Tb (1)9 ,s f * (x)(V1)b (2) sV, 14 4a5 1997 M9 null null9null null null nullnull null null nullCHINESE JOURNAL OF COMPUTATIONAL PHYSICSnull null Vol. 14, No. 4-5 null Sep. , 1997null V1null sFEs x
4、 0 0null5 1 1null5 2 3 5 f * (x) 1 0null882 5 0null606 5 0null324 7 0null135 3 0null011 1 0 !Fn = (1/ 2null)null xn - null exp(- x 2/ 2)dx,i 7F0= 0,5pn= Fn- Fn-1V Ux | uW(xn-1, xn) = qb V|sf * (x)Fs T:f * (x) = null 12 n= 1 pnf *n (x)bB ,L VFZ E LC s , r qnull= 0null801 2,1 = r qnull= 0null250 7 b m
5、 / 3nullMZE#E 3 null Fn-1 null null Fn LCfn(x)Xfn Xf = Xfn | (0,1) uW ( s null1null2,TMX 1= (- 2lnnull1)1/2cos(2nullnull2),X2= (- 2lnnull1)1/2sin(2nullnull2),5X1X2 VN(0,1)s bX1= (- 2lnnull1)1/2cos(2nullnull2),9 V sZEb ZE19 a 7Za?(?), i E *r q5,yN n HiBb kV ,ZE1 E1 8 H,7 FZE n Hv8Mb sME VTt, (Marsagl
6、iaand Brag)4E 3 s b 4nullE(PolarMethod) E1 3 s V/ : (1) 3(0,1) ( s null1null2;i| M(- 1,1) uW ,u= 2null1- 1, v= 2null2- 1b (2)9 W= u2+ v2b (3) TWnull1,5(1);5 (4)9 Z= - 2ln( W)/ W (1/2), |x1= uz,x2= vz,B S s b Xf1 = lnnull1 (Xf1 =Xf sign(null3- 0null5)Xf 1 (+) + 1)2 null - 2lnnull2? (-) null nullZEe L
7、Cb Bt ,i(3) H v21%9 H$ ,19 f (? ?),y7 3 1 yt, ME y10 30%b 5nullZE | s f s T:f( x)= H (x)f 1( x), f 1( x)= exp(- | x| )/ 2,H( x)= 2/nullexp(- x2/2+ | x|)b ms ZEb r qnull= null/ 2enull0null760b Vn,ZE1ME B, 9 b 6null ZE (1)Qf null 2Qf TXF= F- 1(null) null a+ bnull+ cnull2+ null(1- null)2lnnull+ nullnul
8、l2ln(1 - null), a= - 0null826 8, b= 1null673 6,c= 0; null= 0null331 5,null= - 0null331 5b 567null4a5 7: sZE (2)Qf /null1Z ) K sf /3,/ zB ,t=null- 0null5,x= - 2ln| t| ,Xf =(x - a0+ a1x+ a2x 2 1+ b1x+ b2x2+ b3x3)sign( t), a0= 2null515 517, a1= 0null802 853, a2= 0null010 328;b1= 1null432 788,b2= 0null1
9、89 269,b3= 0null001 308bBZE,l10- 4b (3) q (KE) null qd9 , M Xf n = ( null n 1 null1- n2 )/ n12 v s M b 4, n |vb L=,nB |8 12b+Yn = 12 H,Xf 12 = null 12 i= 1 nulli- 6b s ZE, s f 0 ( )aL (|L )a=Q wL ( L )#H(spline) , T , V A 4bN, Marsaglia, MaclarenBrayI !9 B y E V2null+ZE1 ZEn F12null852 32; 1 988 M28
10、null234 16; 698 E14null672 14; 613 Qf /61null898 13; 495 NRT, LC,100 400 VbAhrensDieter ENFL, ENRT1 ,V =iBv,E 7Z# b X ENEA, E1z s M ? 3 ; Y E ENAL,1 T, P E VM5b B ZE, VVn( )ae LCa #_ +8S I n bV2 486, DOS3null3 Td,FORTRAN/,BtZET 1 ( M n /,FORTRAN S3 )b VV2 V A,E BZLrZEb ID 1nullZ.9 E + 5 ZE. , 1988,
11、255 258. 2null ,f0 .9 .S S/ v , 1992, 50 51. 3null Muller M E. A comparison of methods for generating normal deviates on digital computer.JACM,1959,3: 376. 4null ,fm6. + 5 ZE# 0 5. S , 1980, 73 76. 5null ,fm6, .1 3 M ZE8 . + 5 ZE# .S Sv , 1993, 50 57. RANDOMSAMPLINGTECHNIQUESOFTHE NORMALDISTRIBUTION
12、 Gong Ye (Department of Physics, Dalian University of Technology,116024) ABSTRACTnull This paper assesses severalsampling techniques for the normaldistribution. A comparison of various techniques is giv- en for practical applications. KEYWORDSnull the normal distribution; sampling technique; efficiency. 5689null null null nullnull null 14 null
