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.
Thank you advance!!