Does there exist a probability density distribution function with analogous properties to those of the Gaussian distribution, but defined on domains such as:

  1. a limited segment $$x \in [a,b]$$
  2. a circular domain (a domain which "wraps around") $$\theta \in [0, 2\pi)$$

By asking "properties similar to the Gaussian", I would ideally like something as the central limit theorem.

  • $\begingroup$ For 2. check out von Mises distribution also known as the circular normal distribution. $\endgroup$ – Sasha Dec 21 '12 at 13:17
  • $\begingroup$ You might also want to look at central limit theorems in free probability. $\endgroup$ – Eckhard Dec 21 '12 at 13:21

Apparently, you are looking for

  1. von Mises distribution
  2. Wrapped normal distribution

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