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)){xI_0(b)+2sum_(j=1)^infty(I_j(b)sin[j(x-a)])/j},](/images/equations/vonMisesDistribution/NumberedEquation2.svg) |
(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)
|
