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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)=F−1(x;κ)
μ=0μ2=∫π−πx2f(x;κ)dxγ1=0γ2=∫π−πx4f(x;κ)dxμ22−3
This can be used for defining circular variance.
Implementation: scipy.stats.vonmises