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#' WP method background function computeLL
#'
#' This is a background/internal function called by \code{WP}. It computes the log-likelihood.
#'
#' @param NT vector of case counts
#' @param p discretized version of the serial distribution
#' @param R0 basic reproductive ratio
#' @return The function returns the variable \code{LL} which is the log-likelihood at the input variables and parameters.
#'
#' @export
computeLL <- function(p, NT, R0) {
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)
}
mu_t <- R0 * mu_t
LL <- sum(NT[-1] * log(mu_t)) - sum(mu_t)
return(LL)
}
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