贴一个蒙特卡洛方法的matlab程序,供大家使用。! V* N0 [, K4 L& L
祝大家比赛都能取得好成绩 ' h. l/ B7 U( _# M2 T0 X# |0 \/ s* E- g$ [* x7 g$ k
( f# J' s. Y7 ~* U% c
% Example Monte Carlo Simulation in Matlab & h: u, W8 I. Z0 b. W7 v, Q4 x
% Function: y = x2^2/x1 ! l& R# H7 s2 N. a0 K8 Q( \ F6 p% ) L; x+ ~8 s. c" q% G X
% Generate n samples from a normal distribution : z3 d+ w0 v4 ^
% r = ( randn(n,1) * sd ) + mu 7 ~9 d3 ~- v) F h' R& Z
% mu : mean 2 K7 W9 B( L& u2 Z) W- M% sd : standard deviation - m, }' u I5 n$ l+ v8 q- P
% ! o$ P0 ^) A& I) U+ |
% Generate n samples from a uniform distribution 8 l2 w. c# g7 ^% r = a + rand(n,1) * (b-a) " J( w% m4 n5 C1 L0 p# q. n% a : minimum ( _& _4 z w' e% b : maximum H" o9 s' C3 T2 Nn = 100000; % The number of function evaluations 4 r( p# v9 T- D" Z" U% --- Generate vectors of random inputs & T5 W0 |9 P A
% x1 ~ Normal distribution N(mean=100,sd=5) 4 Q1 V! x" C7 F% x2 ~ Uniform distribution U(a=5,b=15) % h3 H% U% O5 u% R" n- e0 M
x1 = ( randn(n,1) * 5 ) + 100; 3 i3 B2 a. y5 ^) o% G" N' ~0 ix2 = 5 + rand(n,1) * ( 15 - 5 ); - L& R4 e6 J; g: ~3 q7 z- l% --- Run the simulation 5 o9 @& p. v; } x% Note the use of element-wise multiplication # z/ {7 D1 o+ @2 o, i
y = x2.^2 ./ x1; , v5 d: _; w; L2 e
% --- Create a histogram of the results (50 bins) $ X ?/ i1 p/ D6 O/ T
hist(y,50); F( B/ \! s( x; K$ _$ N/ K# D% --- Calculate summary statistics $ T+ R. z2 m& @; S& j. l
y_mean = mean(y) ! K3 W* i Q$ X; K0 s6 ^5 k3 Q
y_std = std(y) ) V3 o1 X, a, |3 h" S9 u- ~7 fy_median = median(y)