How to sample from custom 2D distribution?

Question

Filip Trönnberg 2012-4-18

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/35861-how-to-sample-from-custom-2d-distribution

编辑： Ahmadreza Momenisedei 2020-9-28

I have a joint density function for to independent variables X and Y. (See: http://dl.dropbox.com/u/709705/JointDens.png) And I now want to sample new x,y from this distribution.

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.

I also used the matlab-function cumtrapz to find the cumulative distribution function for the above pdf. (See: http://dl.dropbox.com/u/709705/CumulativeDist.png)

Just to be clear, what i want to do is to sample random values x,y from this empirical distribution.

Can someone please point me in the right direction here?!

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Razvan 2012-4-19

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/35861-how-to-sample-from-custom-2d-distribution#answer_45071

Try pinky :)

http://www.mathworks.com/matlabcentral/fileexchange/35797

3 个评论
显示 1更早的评论隐藏 1更早的评论

Tristan Ursell 2012-7-26

Happy to help :)

Hussein Ammar 2019-7-2

Thank you for mentioning this function. It helped me a lot.

请先登录，再进行评论。

Answer 2

Richard Brown 2012-4-19

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/35861-how-to-sample-from-custom-2d-distribution#answer_45092

A really basic, quick to code (but darned inefficient way) is to generate uniform samples in the 3D volume defined by the x and y coordinates and the maximum z coordinate. Accept only samples that fall beneath the surface. The x,y coordinates of these samples will have the distribution you want.

3 个评论
显示 1更早的评论隐藏 1更早的评论

Atul Kedia 2019-7-21

编辑：Atul Kedia 2019-7-22

Lets say the pdf is for variables

and is denoted by

.

You can imagine a 2-D distribution as a surface in 3 dimensions with undulations based on the distribution. The height of the surface above any

point corresponds to its probability (distribution

). What he is suggesting is to sample uniformly over the range of

(where maximum value that z takes = maximum value of the pdf, or

, or the max height of the surface in 3-D).

If for the sampled (

) ,

then the coordinates

are part of your randomly sampled points. If

then the point

need to be rejected and is not part of your sample.

Let me know if you have more questions.

Ahmadreza Momenisedei 2020-9-28

编辑：Ahmadreza Momenisedei 2020-9-28

That was smart!

请先登录，再进行评论。

Answer 3

Tom Lane 2012-4-19

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/35861-how-to-sample-from-custom-2d-distribution#answer_45090

There is a Statistics Toolbox function "slicesample" that could be useful. It does not generate independent samples from the distribution, but instead generates a Markov Chain such that a long sequence of values will have a distribution close to the target distribution. To use this, you would need to be able to write down an expression for the density.