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랜덤 변수 발생 ,중심극한정리

저작시기 2009.06 |등록일 2009.06.08 | 최종수정일 2015.09.18 워드파일MS 워드 (docx) | 8페이지 | 가격 10,000원

소개글

기각법, 중심극한정리, 가우시안 랜덤 변수,
generating random vraibale using transformation method, rejection method,
central limit theorm, 에관련된 자료 입니다.

목차

1) The Inverse Transform Algorithm.
2) The Rejection Method
Reference

본문내용

1) The Inverse Transform Algorithm.
Proposition
Let U be a uniform (0,1) random variable. For any continuous distribution function F the random variable X defined by X=Inv (F (U)) has distribution F.
Proof
Let Fx denote the distribution function of X=Inv (F (U)). Then,
Fx(x) =P{X<=x}
=P {Inv (F (U)) <=x}
Now since F is a distribution function it follows that F(x) is a monotone increasing function of x and so the inequality “a<=b” is equivalent to the inequality “F (a)<=F(b)”.
Hence, we see that
Fx(x)=P{F(inv(F(U)))<=F(x)}
=P {U<=F(x)} (since F(inv(F(U))=U)
=F(x) (since U is uniform (0, 1))

Implementation by using MATLAB


n=10000;
uni=rand(1,n);
X=sqrt(uni)
[N,h]=hist(X,100)
N=N/(h(2)-h(1))./n;
bar(h,N,1,`w`)
hold on

x=0:1;
y=2*x
plot(x,y);

참고 자료

1. Computational statistics handbook, with Matlab, J.E. Gentle Wolfgang Hsrdle
2. Simulation, second edition, Sheldon M.Ross.
3. Main textbook of our class.
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