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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
 
$$
 
$$
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p(\theta) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1))
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p(\phi) = \frac{1}{2\pi I_0(\kappa)} \exp(\kappa \cos(\phi-\theta_1))
 
$$
 
$$
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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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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 normalising factor $I_0(\kappa)$ is an incomplete Bessel function.
  
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The von Mises distribution is commonly used in the statistical analysis of directions.
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The von Mises distribution is commonly used in the statistical analysis of directions. It may be obtained as the hitting density of two-dimensional [[Brownian motion]] with constant drift. 
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====References====
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* Gordon, Louis; Hudson, Malcolm, ''A characterization of the von Mises distribution''  Ann. Stat. '''5''' (1977) {{DOI|10.1214/aos/1176343906}} {{ZBL|0378.62012}}
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* Kendall, David G., ''Pole-seeking Brownian motion and bird navigation'' J. R. Stat. Soc., Ser. B '''36''' (1974) [http://www.jstor.org/stable/2984925] {{ZBL|0291.92005}}
  
 
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Latest revision as of 19:47, 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 normalising factor $I_0(\kappa)$ is an incomplete Bessel function.

The von Mises distribution is commonly used in the statistical analysis of directions. It may be obtained as the hitting density of two-dimensional Brownian motion with constant drift.

References

How to Cite This Entry:
Von Mises distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Von_Mises_distribution&oldid=39994
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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