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I want to use a distribution to predict the p-value (whether it's just noise) of each element in this dataset. But I don't know what distribution should I use. Could anyone give me some tips about it?

The histogram of the data

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    $\begingroup$ 1) What do you mean by "p-value" and "whether it's just noise"? If it's random, and you have no information about why you see e.g. a 1 vs an 0.5 on some observations, it is just noise, or it may as well be. 2) With the sample size you have, that bump around 0.6 is likely to cause you big problems fitting a simple, off-the-shelf distribution. $\endgroup$
    – jbowman
    Jul 12, 2012 at 22:21

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If you want to see if p-values are just noise, you should use the uniform distribution. I think by "just noise" you mean "the null is true".

But where did you get all these p-values? Elements in a data set don't have p-values.

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You probably should use a zero-inflated poisson model or zero-inflated negative binomial distribution. See this question. Another distribution worth considering is the Zipf distribution.

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    $\begingroup$ I don't understand the meaning of your statement that you want to use the distribution "to predict a p-value for every element in this dataset." That makes no sense. $\endgroup$ Jul 12, 2012 at 22:09
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    $\begingroup$ The idea of zero inflation (that is, a mixture of a discrete zero and another distribution) is good, but it does not seem to apply directly. Both ZIP and ZINB are for nonnegative integral responses, which clearly is not the case here. $\endgroup$
    – whuber
    Jul 12, 2012 at 22:25

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