#skewness
circ_skew <- function(theta){
n<-length(theta)
C1 <- sum(cos(theta))
S1 <- sum(sin(theta))
R.bar <- sqrt((C1/n)^2+(S1/n)^2)
theta.bar <- atan2(C1, S1)
rho2 <- sum(cos(2*(theta-theta.bar)))/n
C2 <- sum(cos(2*theta))/n
S2 <- sum(sin(2*theta))/n
mu2 <- atan2(C2, S2)
skew <- (rho2*sin(mu2-2*theta.bar))/(1-R.bar)^3/2
skew
}
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