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My classmate told me:

Any data in this world fit a kind of distribution

I am just newbie in statistics.I just know normal,binorm,poisson,chisq,gamma,beta,etc.
Does humankind discover all distribution in this world?
Where can I get a complete collection of distribution?

WhiteGirl
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  • You might find the discussion in the answers by Tim and myself here and some of the ensuing comments useful -- there's discussion about there being an infinite (indeed uncountable) number of possible distributions. It's not possible to list them all. – Glen_b Jul 10 '17 at 04:51

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It's the same question as if humankind has already discovered all the food recipes. There is no finite number of possible distributions. There is even not a finite number of possible distribution families. You can describe your own and name it after yourself.

Daniel Dostal
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    In the same way that you can, given a piece of food, write a recipe that is simply the list and quantities of ingredients in the food, you can always find a distribution that "fits" any dataset: just compute the empirical distribution. – Chris Haug Jul 09 '17 at 23:32
  • hard to agree.Distribution must has beautiful formula. – WhiteGirl Jul 10 '17 at 00:50
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    @WhiteGirl Why must it? The real world often doesn't work that way. Pretty formulas are nice and all, but actual data are messy. All models are wrong, the famous quote goes, but some are useful. It's a very rare situation where a simple-form distribution is anything better than an approximation. As you get more data, the differences between model and data become more clear (which is why goodness of fit tests tend to reject every "standard" distribution you might think of when the sample size is big enough) – Glen_b Jul 10 '17 at 03:52
  • @Glen_b,it's contradiction.law of large numbers told us, bigger sample size, the more closer to the distribution. I learned from textbook. – WhiteGirl Jul 10 '17 at 04:29
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    I think that you misunderstand what the law of large numbers says. But leaving the actual law of large numbers to one side, it's true that under random sampling and as $n$ approaches the population size (or ∞, if with replacement), the ECDF approaches the population cdf. However there's no reason to think that the population cdf has some neat closed-form formula that's nice to write down. The more data you get, the more certain you can be that the distribution is actually messier than simple formulas. Numerous examples (some with millions of observations) can be found right here on our site. – Glen_b Jul 10 '17 at 04:35
  • A simple refute,the coin toss data must be normal distribution, the more time I toss, the more certain the distribution is normal.You can list your examples. – WhiteGirl Jul 10 '17 at 05:48