von Mises Distribution
المؤلف:
Evans, M.; Hastings, N.; and Peacock, B.
المصدر:
"von Mises Distribution." Ch. 41 in Statistical Distributions, 3rd ed. New York: Wiley
الجزء والصفحة:
...
16-4-2021
2100
von Mises Distribution
A continuous distribution defined on the range 
with probability density function
 |
(1)
|
where 
is a modified Bessel function of the first kind of order 0, and distribution function
![D(x)=1/(2piI_0(b))<span style=]() {xI_0(b)+2sum_(j=1)^infty(I_j(b)sin[j(x-a)])/j}, " src="https://mathworld.wolfram.com/images/equations/vonMisesDistribution/NumberedEquation2.gif" style="height:49px; width:318px" /> |
(2)
|
which cannot be done in closed form. Here, 
is the mean direction and 
is a concentration parameter. The von Mises distribution is the circular analog of the normal distribution on a line.
The mean is
 |
(3)
|
and the circular variance is
 |
(4)
|
REFERENCES:
Evans, M.; Hastings, N.; and Peacock, B. "von Mises Distribution." Ch. 41 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 189-191, 2000.
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