#kappa estimation (concentration parameter of von-Mises distribution)
vm_kappa <- function(theta){
theta <- na.omit(theta)
n<-length(theta)
C1 <- sum(cos(theta))
S1 <- sum(sin(theta))
R.bar <- sqrt((C1/n)^2+(S1/n)^2)
kappa <- function(R.bar){
if(R.bar<0.53){k<-2*R.bar+R.bar^3+5*R.bar/6
return(k)}
else if((R.bar>=0.53)&&(R.bar<0.85)){k <- -0.4+1.39*R.bar+0.43/(1-R.bar)
return(k)}
else if(R.bar>=0.85){k<- 1/(R.bar^3-4*R.bar^2+3*R.bar)
return(k)}
}
kappa(R.bar)
}
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