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SciPy

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Von Mises Distribution

Defined for x[π,π] with shape parameter κ>0 . Note, the PDF and CDF functions are periodic and are always defined over x[π,π] regardless of the location parameter. Thus, if an input beyond this range is given, it is converted to the equivalent angle in this range. For values of κ<100 the PDF and CDF formulas below are used. Otherwise, a normal approximation with variance 1/κ is used.

f(x;κ)=eκcosx2πI0(κ)F(x;κ)=12+x2π+k=1Ik(κ)sin(kx)I0(κ)πkG(q;κ)=F1(x;κ)
μ=0μ2=ππx2f(x;κ)dxγ1=0γ2=ππx4f(x;κ)dxμ223

This can be used for defining circular variance.

Implementation: scipy.stats.vonmises