207.70.163.210: /* Pair of "E" cores */

2015-01-05T21:14:40Z

Pair of "E" cores

Show changes

en>FrescoBot: Bot: link syntax and minor changes

2014-02-10T08:12:44Z

Bot: link syntax and minor changes

Show changes

en>DaveeBlahBlah: Added image at bottom of lead that shows the electronic symbols for magnetic cores

2014-02-04T05:35:25Z

Added image at bottom of lead that shows the electronic symbols for magnetic cores

New page

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 {{nowrap|[ 0,  2π ) }}.<ref name=D>Dodge, Y. (2006) ''The Oxford Dictionary of Statististical Terms'', OUP. ISBN 0-19-920613-9</ref> A circular distribution is often a [[continuous probability distribution]], and hence has a [[probability density function|probability density]], but such distributions can also be [[discrete probability distribution|discrete]], in which case they are called '''circular lattice distributions'''.<ref name=D/> 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.

==Graphical representation==

If a circular distribution has a density

:<math>p(\phi) \qquad \qquad (0\le\phi<2\pi),\,</math>

it can be graphically represented as a closed [[curve]]

:<math>[x(\phi),y(\phi)] = [r(\phi)\cos\phi, \, r(\phi)\sin\phi], \, </math>

where the radius <math>r(\phi)\,</math> is set equal to
:<math>r(\phi) = a+b p(\phi), \, </math>

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 lobe-shaped polar distribution emerges. The main direction of the lobe in the
first quadrant corresponds to the [[slant (handwriting)|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]]
*[[Directional statistics#Circular and higher dimensional distributions]]

==References==
{{reflist}}

==External links==
* [http://www.codeproject.com/Articles/190833/Circular-Values-Math-and-Statistics-with-Cplusplus Circular Values Math and Statistics with C++11], A C++11 infrastructure for circular values (angles, time-of-day, etc.) mathematics and statistics

{{ProbDistributions|families}}

[[Category:Types of probability distributions]]
[[Category:Statistical charts and diagrams]]

Magnetic core - Revision history

207.70.163.210: /* Pair of "E" cores */

en>FrescoBot: Bot: link syntax and minor changes

en>DaveeBlahBlah: Added image at bottom of lead that shows the electronic symbols for magnetic cores