模拟联合累积分布函数中的样本? [英] Simulate samples from a joint cumulative distribution function?
问题描述
我有一个联合密度函数，用于两个独立变量X和Y.现在，我想从此分布中采样新的x，y.
I have a joint density function for two independent variables X and Y. And I now want to sample new x,y from this distribution.
我认为我要做的是找到联合累积分布，然后以某种方式抽样.我有点知道如何在一维中执行此操作，但是我发现很难理解如何在二维中执行此操作.
What I believe I have to do is to find the joint cumulative distribution and then somehow sample from it. I kinda know how to do this in 1D, but I find it really hard to understand how to do it in 2D.
我还使用了matlab函数cumtrapz来找到累积分布函数以上pdf.
I also used the matlab function cumtrapz to find the cumulative distribution function for the above pdf.
请明确一点，我要做的是从该经验分布中采样随机值x，y.
Just to be clear, what i want to do is to sample random values x,y from this empirical distribution.
有人可以在这里向我指出正确的方向吗?！
Can someone please point me in the right direction here?!
编辑:我有数据值，并且使用 [pdf bin] = hist3([N Y])
I have data values and I use [pdf bins] = hist3([N Y])
然后我将pdf规范化并做
I then normalize the pdf and do
cumulativeDistribution = cumtrapz(pdfNormalize)
cumulativeDistribution = cumtrapz(pdfNormalize)
是的(在下面的评论中)X，Y应该是独立的.
And yes (to the comment below) X,Y are suppose to be independent.
推荐答案
如果您知道如何对1D分布进行采样，则可以将其扩展到2D.为 X 创建边际分布.从中获取一个样本，例如 X 1 .然后在2D分布中修复一个变量X = X 1 并为 Y 采样，即从中采样 Y 一维分布f XY ( X 1 ， Y ).
If you know how to sample a distribution in 1D then you can extend it to 2D. Create the marginal distribution for X. Take a sample from that, say X1. Then in your 2D distribution fix one variate X=X1 and sample for Y, i.e., sample Y from 1D distribution fXY(X1, Y).
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