# What kind of distribution is it?

I was trying to help my colleague with fitting a distribution curve to some empiric data. However, I haven't succeeded since it's my first experience in approximating an empiric distribution with a theoretical one.

The mean value of $Y$ is 0.32688.

$\sigma^2_Y$ is 0.076191.

Here's a histogram:

And an empirical cdf:

There are 1024 samples in the data.

Obviously the distribution is asymmetric. It doesn't look like $\chi^2$ since $\hat{\mu}_Y >> 2\hat{\sigma}_Y^2$

I tried approximating it with beta distribution (picked various $\alpha, \beta$ parameters) together with normalizing Y by some real number in $[0.5; 3]$. It didn't help, Pearson chi-squared statistic was always, you know, like 300, 700 or even more.

I tried squaring Y and the histogram of $Y^2$ looks like this:

I tried approximating this with exponential distribution (and normalizing Y with a real number) - but P-value was always like zero all the time.

Does anyone have any ideas on what distribution this data could have?

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due to its bimodal shape, you might want to try a gaussian mixture-model (weighted sum of two gaussians)? –  thias Dec 19 '11 at 11:42
Where do these data come from? (That is, how do they arise?) –  cardinal Dec 19 '11 at 12:48
My colleague is studying at university. His professor claims that these are sea water level observations, but doesn't give any more details. n=1024 may even mean that the data is artificial. –  wh1t3cat1k Dec 19 '11 at 14:18
Why do you need to "fit a distribution curve"? It is rare that arbitrary curve fitting is of much help and when it is, that is because the fit is good, simple, and clear, which appears to be a highly unlikely outcome in this case. –  whuber Dec 19 '11 at 14:55
I followed up on thias suggestion, using the package Mclust in R, and came up with a best fit (using BIC as a criterion) of a mixture of 5 Gaussians. It's nice to have a simple functional formula for a distribution, but I agree with thias and whuber - it isn't necessary or, in this case, at all likely that you'll be able to come up with one for this data. –  jbowman Dec 19 '11 at 17:35
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