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I have a probability mass function of some experimental data who's log looks like the following: (please ignore the fact that it is not normalized) ![alt text][1]

[image shack image removed]

(meaning if p(x) is the pmf, this is log(p(x)) ) Does anyone know what parametric family it might belong to? (note that this is a discrete distribution)

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closed as unclear what you're asking by Stefan Kohl, quid, Marco Golla, Chris Godsil, Alex Degtyarev Aug 30 '15 at 9:41

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

The graph kind of looks like a rotated Fermi-Dirac distribution... Can you give some information about where this data is coming from? Do you have any theoretical model to compare it to? – Alberto García-Raboso Feb 9 '10 at 22:14
if anything it is more of an inverse sigmoid. It came from the distribution of certain image features after they have been quantized (it is the distribution of a sort of 'visual vocabulary'). The distribution is from a large database of images with no special characteristic (natural + synthetic images). – liza Feb 9 '10 at 22:30
So the y axis is log-number of features falling in a particular bin, and X is just feature index sorted by popularity? – user3035 Feb 9 '10 at 22:44
Alas, without the image, it's pretty much impossible to tell what this old question is asking. The only answer below suffers from the same problem too. – Ilmari Karonen Aug 29 '15 at 21:27
Since without the image the question is meaningless, and since the OP has visited the site for the last time 4 years ago, I am voting to close as "unclear what you're asking". – Stefan Kohl Aug 29 '15 at 22:35

I tried taking the logarithm to the pdf of a $\beta(0.5, 1.5)$ (see Beta distribution) and it gave me this

[image shack image removed]

Maybe this can be fitted for your data.

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The Beta-family seems a really good guess, though at this point it is just what it is: an educated guess. If liza could explain to us what and how has been measured, we might say more :). – fedja Feb 22 '10 at 15:59
Very interesting! I'll try it – liza Feb 23 '10 at 20:37

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