2
$\begingroup$

Cross post from Stats.SE: https://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.

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.