Goodness of fit of two different distributions to one set of data


New Member
Hi all,

I have a set of data so I am willing to fit a distribution to this set of data. Now the ones in consideration are the Gaussian and the Von Mises distributions respectively. I have done most of the stuff needed and in my case i have seen (visually) that the Von Mises fits my data better. It is a long procedure so I prefer not to go through everything. My question is:

Is there any way to quantitavely prove that the Von Mises is better than the Gaussian? I am aware of the individual Goodness of Fit tests for each of the distributions but as I understand this is not a common measure of both. As a result I cannot say that e.g. the Von Mises is 2.3% better overall or something similar.

I hope you understand my problem

Any thoughts will be very much appreciated


Hi Alex,

I can't reply directly to question of proving that one distribution is better, but I'm wondering whether the data itself would tell you which distribution to use.

As I understand it, the von Mises distribution is nearly identical to the normal distribution in the bell shape of it's PDF, except that von Mises is used for data that is measured as the angles of a circle. If your data is of this nature, then I guess it makes sense to use it.


TS Contributor
I can't answer directly,either. But I think that a pretty "raw" indicator would be the value of the test-statistic. But this could be useful only in extreme differences (e.g both p-values accept the fit but one of them is much closer to your sig, level).

Hope I helped (but I doubt:))