# Goodness of fit test for bivariate distribution?

I have a dataset which is x-y distributed, and I fitted a model for it. (see below, left and right)

How can I test the goodness of fit for the model I fitted?

### What I've done:

After searching for a while, I found this http://arxiv.org/abs/1102.2407 , which is a good summery of existing approaches. And it seems still a big problem to be solved?

I also read http://www.sciencedirect.com/science/article/pii/S0167715297000205, which is a multivariate K-S test. And it is cited a lot. I may give it a try.

Notice:

I have ask this question here, but it didn't receive too much attention, so I re-posted here, hope someone can give any advice.

• Please provide short description of the papers (what you learned from them, what is unclear) since people are not going to read them only to answer your question. Also, the papers seem to answer your question directly so please tell us why they do not fit you. – Tim Jan 2 '16 at 9:29
• @Tim, Yes, I've updated my description. I may try the K-S approach. But still want to know other mature approaches, since I'm not very familiar with this field. – cqcn1991 Jan 2 '16 at 9:36
• The papers answer your question directly and for sure they provide more detailed answer than you can possibly get on such site like CV (that very unlikely would be longer than one printed page). So what exactly do you want to know? – Tim Jan 2 '16 at 9:40
• @Tim, Well, this is just the method that I found. But I'm not sure if this are the mature approach people use. So I'm posting here to see people's opinoin. Maybe I found a good approach, or maybe there're other good way of doing it as well. – cqcn1991 Jan 2 '16 at 9:45
• You should write up the papers you cite in an answer. Visually the fit looks pretty good to me, but it takes more context to know if it is good enough for your purposes. – Andy W Jan 2 '16 at 14:44