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-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/WP.R
-\name{WP}
-\alias{WP}
-\title{WP method}
-\usage{
-WP(
-  NT,
-  mu = NA,
-  search = list(B = 100, shape.max = 10, scale.max = 10),
-  tol = 0.999
-)
-}
-\arguments{
-\item{NT}{Vector of case counts.}
-
-\item{mu}{Mean of the serial distribution (needs to match case counts in time
-units; for example, if case counts are weekly and the serial
-distribution has a mean of seven days, then \code{mu} should be set
-to one). The default value of \code{mu} is set to \code{NA}.}
-
-\item{search}{List of default values for the grid search algorithm. The list
-includes three elements: the first is \code{B}, which is the
-length of the grid in one dimension; the second is
-\code{scale.max}, which is the largest possible value of the
-scale parameter; and the third is \code{shape.max}, which is
-the largest possible value of the shape parameter. Defaults to
-\code{B = 100, scale.max = 10, shape.max = 10}. For both shape
-and scale, the smallest possible value is 1/\code{B}.}
-
-\item{tol}{Cutoff value for cumulative distribution function of the
-pre-discretization gamma serial distribution. Defaults to 0.999
-(i.e. in the discretization, the maximum is chosen such that the
-original gamma distribution has cumulative probability of no more
-than 0.999 at this maximum).}
-}
-\value{
-\code{WP} returns a list containing the following components:
-        \code{Rhat} is the estimate of R0, and \code{SD} is either the
-        discretized serial distribution (if \code{mu} is not \code{NA}), or
-        the estimated discretized serial distribution (if \code{mu} is
-        \code{NA}). The list also returns the variable \code{check}, which is
-        equal to the number of non-unique maximum likelihood estimators. The
-        serial distribution \code{SD} is returned as a list made up of
-        \code{supp} (the support of the distribution) and \code{pmf} (the
-        probability mass function).
-}
-\description{
-This function implements an R0 estimation due to White and Pagano (Statistics
-in Medicine, 2008). The method is based on maximum likelihood estimation in a
-Poisson transmission model. See details for important implementation notes.
-}
-\details{
-This method is based on a Poisson transmission model, and hence may be most
-most valid at the beginning of an epidemic. In their model, the serial
-distribution is assumed to be discrete with a finite number of posible
-values. In this implementation, if \code{mu} is not {NA}, the serial
-distribution is taken to be a discretized version of a gamma distribution
-with mean \code{mu}, shape parameter one, and largest possible value based on
-parameter \code{tol}. When \code{mu} is \code{NA}, the function implements a
-grid search algorithm to find the maximum likelihood estimator over all
-possible gamma distributions with unknown mean and variance, restricting
-these to a prespecified grid (see \code{search} parameter).
-
-When the serial distribution is known (i.e., \code{mu} is not \code{NA}),
-sensitivity testing of \code{mu} is strongly recommended. If the serial
-distribution is unknown (i.e., \code{mu} is \code{NA}), the likelihood
-function can be flat near the maximum, resulting in numerical instability of
-the optimizer. When \code{mu} is \code{NA}, the implementation takes
-considerably longer to run. Users should be careful about units of time
-(e.g., are counts observed daily or weekly?) when implementing.
-
-The model developed in White and Pagano (2008) is discrete, and hence the
-serial distribution is finite discrete. In our implementation, the input
-value \code{mu} is that of a continuous distribution. The algorithm
-discretizes this input when \code{mu} is not \code{NA}, and hence the mean of
-the serial distribution returned in the list \code{SD} will differ from
-\code{mu} somewhat. That is to say, if the user notices that the input
-\code{mu} and output mean of \code{SD} are different, this is to be expected,
-and is caused by the discretization.
-}
-\examples{
-# Weekly data.
-NT <- c(1, 4, 10, 5, 3, 4, 19, 3, 3, 14, 4)
-
-# Obtain R0 when the serial distribution has a mean of five days.
-res1 <- WP(NT, mu = 5 / 7)
-res1$Rhat
-
-# Obtain R0 when the serial distribution has a mean of three days.
-res2 <- WP(NT, mu = 3 / 7)
-res2$Rhat
-
-# Obtain R0 when the serial distribution is unknown.
-# NOTE: This implementation will take longer to run.
-res3 <- WP(NT)
-res3$Rhat
-
-# Find the mean of the estimated serial distribution.
-serial <- res3$SD
-sum(serial$supp * serial$pmf)
-
-}