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贴一个蒙特卡洛方法的matlab程序,供大家使用。! N Z" O0 \7 c5 Z1 A1 r. k' F
祝大家比赛都能取得好成绩 % f& S9 @( ~. u0 f! N/ {- j
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" ?7 }8 _! U+ u- T8 q3 O% Example Monte Carlo Simulation in Matlab ; h' I7 C6 J3 S& _' r) e% v+ V3 t
% Function: y = x2^2/x1 / @) ^% _: }+ Z9 w1 Q
%
/ p) Q, N3 [, _3 S9 I0 @+ X% Generate n samples from a normal distribution # U% B' T' [$ W/ e- M
% r = ( randn(n,1) * sd ) + mu ^: k% ^5 {4 n9 ]- `
% mu : mean / z, q& ~5 `8 Z1 ]
% sd : standard deviation 0 \- V2 p k- s& p5 Y; F$ a2 z* ~
%
& P. L# Q( N3 N: m% Generate n samples from a uniform distribution * X, ^- Y! g: A0 ~7 r
% r = a + rand(n,1) * (b-a)
3 Y7 h6 ]& \0 u% a : minimum : h3 m3 F& \6 }
% b : maximum 5 i6 u" x3 G8 ]/ l: @1 v o
n = 100000; % The number of function evaluations
& T- w' O( E! f$ ^! F, P5 q+ v. h% --- Generate vectors of random inputs
( {& q7 s: Q k" p% x1 ~ Normal distribution N(mean=100,sd=5) 6 Z9 r7 E5 _9 _. |# v; {" r
% x2 ~ Uniform distribution U(a=5,b=15) 7 {9 i# g2 B( w; J; o$ R# O
x1 = ( randn(n,1) * 5 ) + 100;
/ B2 n8 d- c, q/ e: a* fx2 = 5 + rand(n,1) * ( 15 - 5 ); + s, G; [7 X9 O$ B8 W; V' v
% --- Run the simulation 1 F7 U0 y& [) I: Z
% Note the use of element-wise multiplication
" r5 i ~7 P9 U# l' }9 M/ Cy = x2.^2 ./ x1;
& o* _# J8 E0 V1 ?& K& j% ^% --- Create a histogram of the results (50 bins) ( {: s/ Z- f/ h: @; g8 u' _
hist(y,50); & ~" C: h+ ?+ y- q2 ]" Y9 T
% --- Calculate summary statistics
1 B% J# z: y" F+ B8 w% ^' T! [! ty_mean = mean(y)
8 W ~# a0 c& m# V/ S" K6 sy_std = std(y) - d9 z5 h0 ?0 @, A
y_median = median(y) |
zan
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