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Difference between revisions of "Von Mises distribution"

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''circular normal distribution''
 
''circular normal distribution''
  
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A unimodal [[Probability distribution|probability distribution]] on the circle with probability density
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A unimodal [[probability distribution]] on the circle with probability density
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$$
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p(\theta) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1))
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$$
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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. 
  
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200501.png" /></td> </tr></table>
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The von Mises distribution is commonly used in the statistical analysis of directions.
  
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with two parameters, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200502.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200503.png" />. This function takes its maximum value at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200504.png" />, so that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200505.png" /> is the mode; <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/v/v120/v120050/v1200506.png" /> is a concentration parameter.
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The von Mises distribution is the most frequently used probability distribution in the statistical analysis of directions.
 

Revision as of 19:34, 13 December 2016

circular normal distribution

A unimodal probability distribution on the circle with probability density $$ p(\theta) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1)) $$ 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=11488
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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