[英]Random variable from pdf in matlab
I want to simulate some random variables distributed as a Variance Gamma. 我想模拟一些作为方差Gamma分布的随机变量。
I know the pdf ( http://en.wikipedia.org/wiki/Variance-gamma_distribution ) but I don't know the inverse of the cumulative function F: so I can't generate a random uniform variable U and compute x=F^(-1)(U).
我知道pdf( http://en.wikipedia.org/wiki/Variance-gamma_distribution ),但我不知道累积函数F的反函数:因此,我无法生成随机的统一变量U并计算
x=F^(-1)(U).
I have to do this in MATLAB. 我必须在MATLAB中执行此操作。
Thank you! 谢谢!
Stefano 斯特凡诺
The next natural alternative to look into is Von Neumann's "acceptance-rejection method". 接下来要考虑的另一种自然选择是冯·诺伊曼(Von Neumann)的“拒绝接受方法”。
If you can find a density g
defined on the same space as your f
such that 如果您发现在与
f
相同的空间上定义的密度g
,从而
g
, and g
生成样本,以及 then you are good to go. 那你就好了
If you search the literature, people must have done this. 如果您搜索文献,人们一定已经做到了。 The VG is widely used in pricing options.
VG在定价选项中广泛使用。
Following @Drake 's idea: for the first step you can use Marsaglia and Tsang's Method from here . 遵循@Drake的想法:第一步,可以从此处使用Marsaglia和Tsang的Method。
This is the code to generate gamma random numbers: 这是生成伽玛随机数的代码:
function x=gamrand(alpha,lambda)
% Gamma(alpha,lambda) generator using Marsaglia and Tsang method
% Algorithm 4.33
if alpha>1
d=alpha-1/3; c=1/sqrt(9*d); flag=1;
while flag
Z=randn;
if Z>-1/c
V=(1+c*Z)^3; U=rand;
flag=log(U)>(0.5*Z^2+d-d*V+d*log(V));
end
end
x=d*V/lambda;
else
x=gamrand(alpha+1,lambda);
x=x*rand^(1/alpha);
end
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