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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

(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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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
Sigmoids ( en.wikipedia.org/wiki/Sigmoid_function ) are all over the place in probability laws. You should try to fit the examples linked to in Wikipedia. –  Steve Huntsman Feb 9 '10 at 22:21
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
sheldon: exactly –  liza Feb 9 '10 at 22:47
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1 Answer

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


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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