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    <p>(Answer edited to add additional explanation)</p> <ol> <li><p>You can't really find "the" distribution; the actual distribution from which data are drawn can nearly always* be guaranteed not to be in any "laundry list" provided by any such software. At best you can find "a" distribution (more likely several), one that is an adequate description. Even if you find a great fit there are always an infinity of distributions that are arbitrarily close by. Real data tends to be drawn from heterogeneous mixtures of distributions that themselves don't necessarily have simple functional form.</p> <p>* an example where you might hope to is where you know the data were actually <em>generated</em> from exactly one distribution on a list, but such situations are extremely rare.</p></li> <li><p>I don't think just comparing likelihoods is necessarily going to make sense, since some distributions have more parameters than others. AIC might make more sense, except that ...</p></li> <li><p>Attempting to identify a "best fitting" distribution from a list of candidates will tend to produce overfitting, and unless the effect of such model selection is accounted for properly will lead to overconfidence (a model that looks great but doesn't actually fit the data not in your sample). There are such possibilities in R (the package <code>fitdistrplus</code> comes to mind), but as a common practice I would advise against the idea. If you must do it, use holdout samples or cross-validation to obtain models with better generalization error.</p></li> </ol>
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    1. POGiven a set of random numbers drawn from a continuous univariate distribution, find the distribution
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    1. COAre you suggesting that extra parameters may allow one to "over-fit" the data, and thus achieve an undesireably low loglik?
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    2. CO@unutbu Not necessarily over-fit; but more parameters means more degrees of freedom to fit the data.
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    3. COOverfitting is precisely what happens, yes. You need actual model selection here, which penalises models with greater number of parameters.
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