# Fix domain of von Mises distribution (Distributions.jl) to -π ~ + π

I am analyzing circular mixture time series data which the domain is \pm \pi.
I am planning to use von Mises distribution in HMMBase.jl ( or Turing.jl) to estimate the parameters(e.g. \mu, \kappa) of my data.

In Distributions.jl, probability density function(PDF) is fixed to \pm \pi but cumulative density function(CDF) is not.
It seems to be shifted depending on \mu.

I want to fix the domain of PDF and CDF to \pm \pi whatever the parameter \mu \ ( -\pi \leq \mu \leq \pi) is.
I think I have to implement new bounded von Mises distribution referencing Distributions.jl/vonmises.jl.
In vonmises.jl above, CDF is implemented by integration method shown in wikipedia(von Mises distribution).

I can’t figure out how to achieve my purpose…
Any help would be greatly appreciated.