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#' WP method background function WP_known
#'
#' This is a background/internal function called by \code{WP}. It computes the maximum likelihood estimator of R0 assuming that the serial distribution is known and finite discrete.
#'
#' @param NT vector of case counts
#' @param p discretized version of the serial distribution
#' @return The function returns \code{Rhat}, the maximum likelihood estimator of R0.
#' @export
#
WP_known <- function(NT, p){
k <- length(p)
TT <- length(NT)-1
mu_t <- rep(0, TT)
for(i in 1:TT){
Nt <- NT[i:max(1,i-k+1)]
# print(Nt)
# print(p[1:min(k,i)])
mu_t[i] <- sum(p[1:min(k,i)]*Nt)
}
Rhat <- sum(NT[-1])/sum(mu_t)
return(list(Rhat=Rhat))
}
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