The wrapped normal distribution (or wrapped up normal distribution) occurs via Brownian motion on a circle. It is the circular analog of a normal distribution, achieved by wrapping the probability density function (PDF) of a real-valued, linear random variable to the circumference of a unit circle an infinite number of times .
Formula of the Wrapped Normal Distribution
The density of the wrapped normal distribution can be defined as the series 
Where N is the normal distribution being wrapped and
- μ = mean (taken as modulo 2 π)
- σ = standard deviation.
The density is normalized because integrating it over 2 π is equivalent to integrating the normal distribution over the reals.
Early works define the distribution in different ways. For example, Haight’s 1958 reference work for the National Bureau of Statistics  defines the wrapped up normal distribution as:
Stephens  made a brief mention of the wrapped up normal distribution in his 1958 paper Random Walk on a Circle. He defines it slightly differently, as “of the type”
Stephens also notes that when on a sphere, the wrapped up normal distribution is similar to the Riemann theta (presumably, the Riemann theta function).
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 Pfaff, F. (2019). Multitarget Tracking Using Orientation Estimation for Optical Belt Sorting. KIT Scientific Publishing
 Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.
 Stephens, M.A. (1963). Random Walk on a Circle. Biometrika Vol. 50, No. 3/4 (Dec.), pp. 385-390 (6 pages)