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I'm interested in collecting real-world examples of probability distributions, and heuristics for when a probability distribution might apply.

For example:

  1. Stock prices are often modeled with lognormal distributions, assuming stock returns are normally distributed. More generally, lognormal distributions often apply when there's a proportional effect going on; that is, when the change in object X is proportional to object X's current size.

  2. If your data is skewed (e.g., prices are skewed to the right, since they're required to be positive), then a lognormal distribution might be good to try.

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Please don't post two topics in a row on very similar subjects. I would personally appreciate it if you would somehow figure out a way to merge them. I'm not going to downvote, since it's apparent that you read the FAQ because you community wiki'd both posts. –  Harry Gindi Dec 11 '09 at 1:18
This book may be of some use: Handbook of Statistical Distributions with Applications K. Krishnamoorthy published by Chapman & Hall –  Joseph Malkevitch Dec 11 '09 at 1:28
Please ask a question, then flag for reopening. –  Scott Morrison Dec 11 '09 at 2:01
@Scott: Just curious, how is this different from the post asking for examples of algebraic structures? mathoverflow.net/questions/3242/… –  fraedhur Dec 11 '09 at 2:31
Well, first thing is, it's not technically a question. Second thing is, it's not specific enough and borders on being vacuous (I'm not calling you dumb, I'm saying that the criteria you stated are too weak to restrict past trivial examples). –  Harry Gindi Dec 11 '09 at 2:59
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closed as not a real question by Scott Morrison Dec 11 '09 at 2:00

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

2 Answers

Of course the normal (Gaussian) distribution comes up frequently due to the central limit theorem. However, the normal distribution usually only describes the "middle" well; its tails are often too thin to model the probability of rare events well.

Stable distributions, such as Cauchy, come up when aggregating power law data due to a generalized central limit theorem.

Survival time with constant hazard: exponential.

Survival time with increasing or decreasing hazard: Weibull.

Angela Duckworth argues that "achievement" (nice, broad term) is often distributed as lognormal in a nice 90-second video.

Count data is often Poisson distributed, unless there's overdispersion and then negative binomial may fit better.

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T. Tao wrote a very interesting article on Zipf/Pareto distributions.

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