Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Cross post from Stats.SE: http://stats.stackexchange.com/questions/29601/statistic-for-goodness-of-fit-to-a-multidimensional-distribution-with-geometric

Essentially a reference request, since someone must already have studied this...

I have a model which predicts some probabilities $p_{mn}$, which tends to decay geometrically for large $m$ and $n$. I also have some data $f_{mn}$ of counts when $(m,n)$ occurs. Is there a standard goodness of fit, preferably which reports a $p$-value, suitable for a biological audience?

Personally, I've been calculating the $G$-value: $$G = 2 \sum_{mn} f_{mn} \log\left(\frac{f_{mn}}{N p_{mn}}\right)$$ where $N$ is the sum of $f_{mn}$, and simulating the distribution by Monte-Carlo, and deriving a $p$-value that way. However, given the lack of real analytical understanding, even I don't completely trust it. Is there literature on the behaviour of this statistic? Notice that this converges to the standard $G$-test for a multinomial distribution (finite range for $m$ and $n$) and for large $f_{mn}$ it converges to $\chi^2$-test, so really it is the infinite range which is novel.

share|improve this question

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.