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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 the maximum likelihood estimator of R0.
#'
#' @keywords internal
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)]
mu_t[i] <- sum(p[1:min(k, i)] * Nt)
}
Rhat <- sum(NT[-1]) / sum(mu_t)
return(Rhat)
}
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