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#' Conversion between cumulants and moments
#'
#' Implements conversion between the first four cumulants and moments
#'
#' @param k numeric, first four cumulants.
#' @param m numeric, first four moments.
#'
#' @return numeric
#'
#' @keywords moments
#'
#' @author Stephen H-T. Lihn
#'
#' @export k2mnt
#' @export mnt2k
#'
### <======================================================================>
k2mnt <- function(k) {
m1 <- k[1]
m2 <- k[2]+k[1]^2
m3 <- k[3]+3*k[2]*k[1]+k[1]^3
m4 <- k[4]+4*k[3]*k[1]+3*k[2]^2+6*k[2]*k[1]^2+k[1]^4
c(m1,m2,m3,m4)
}
### <---------------------------------------------------------------------->
#' @rdname k2mnt
mnt2k <- function(m) {
k1 <- m[1]
k2 <- m[2]-m[1]^2
k3 <- m[3]-3*m[2]*m[1]+2*m[1]^3
k4 <- m[4]-4*m[3]*m[1]-3*m[2]^2+12*m[2]*m[1]^2-6*m[1]^4
c(k1,k2,k3,k4)
}
### <---------------------------------------------------------------------->
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