Difference between revisions of "Von Mises distribution"
From Encyclopedia of Mathematics
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p(\phi) = \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)) | ||
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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. | + | 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. | + | 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==== | ||
| + | * Gordon, Louis; Hudson, Malcolm, ''A characterization of the von Mises distribution'' Ann. Stat. '''5''' (1977) {{DOI|10.1214/aos/1176343906}} {{ZBL|0378.62012}} | ||
| + | * 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
- Gordon, Louis; Hudson, Malcolm, A characterization of the von Mises distribution Ann. Stat. 5 (1977) DOI 10.1214/aos/1176343906 Zbl 0378.62012
- Kendall, David G., Pole-seeking Brownian motion and bird navigation J. R. Stat. Soc., Ser. B 36 (1974) [1] Zbl 0291.92005
How to Cite This Entry:
Von Mises distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Von_Mises_distribution&oldid=39996
Von Mises distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Von_Mises_distribution&oldid=39996
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article