In probability and statistics, a circular distribution or polar distribution is a probability distribution of a random variable whose values are angles, usually taken to be in the range [0, 2π).^{[1]} A circular distribution is often a continuous probability distribution, and hence has a probability density, but such distributions can also be discrete, in which case they are called circular lattice distributions.^{[1]} Circular distributions can be used even when the variables concerned are not explicitly angles: the main consideration is that there is not usually any real distinction between events occurring at the lower or upper end of the range, and the division of the range could notionally be made at any point.
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Contents
Graphical representation
If a circular distribution has a density
it can be graphically represented as a closed curve
where the radius is set equal to
and where a and b are chosen on the basis of appearance.
Example
By computing the probability distribution of angles along a handwritten ink trace, a lobeshaped polar distribution emerges. The main direction of the lobe in the first quadrant corresponds to the slant of handwriting (see: graphonomics).
An example of a circular lattice distribution would be the probability of being born in a given month of the year, with each calendar month being thought of as arranged round a circle, so that "January" is next to "December".
See also
 Circular mean
 Circular uniform distribution
 von Mises distribution
 Directional statistics#Circular and higherdimensional distributions
References
 ^ ^{a} ^{b} Dodge, Y. (2006). The Oxford Dictionary of Statistical Terms. OUP. ISBN 0199206139.
External links
 Circular Values Math and Statistics with C++11, A C++11 infrastructure for circular values (angles, timeofday, etc.) mathematics and statistics