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Difference between revisions of "Von Mises distribution"

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A unimodal [[probability distribution]] on the circle with probability density
 
A unimodal [[probability distribution]] on the circle with probability density
 
$$
 
$$
p(\theta) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1))
+
p(\phi) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1))
 
$$
 
$$
 
with two parameters, $\kappa$ and $\theta_1$. This function takes its maximum value at $\phi = \theta_1$, so that $\theta_1$ is the mode; $\kappa$ is a concentration parameter.   
 
with two parameters, $\kappa$ and $\theta_1$. This function takes its maximum value at $\phi = \theta_1$, so that $\theta_1$ is the mode; $\kappa$ is a concentration parameter.   

Revision as of 19:37, 13 December 2016

circular normal distribution

A unimodal probability distribution on the circle with probability density $$ p(\phi) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1)) $$ with two parameters, $\kappa$ and $\theta_1$. This function takes its maximum value at $\phi = \theta_1$, so that $\theta_1$ is the mode; $\kappa$ is a concentration parameter.

The von Mises distribution is commonly used in the statistical analysis of directions.

How to Cite This Entry:
Von Mises distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Von_Mises_distribution&oldid=39995
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article