#' @title CBM AUC function
#'
#' @description {Returns the CBM ROC-AUC
#' See also \code{\link{UtilAnalyticalAucsRSM}}, \code{\link{UtilAucPROPROC}} and \code{\link{UtilAucBIN}}}
#'
#' @param mu The \code{mu} parameter of CBM (separation of non-diseased
#' and diseased pdfs)
#' @param alpha The \code{alpha} parameter of CBM, i.e., the fraction
#' of diseased cases on which the disease is visible
#'
#'
#' @return CBM-predicted ROC-AUC for the specified parameters
#'
#' @examples
#' mu <- 2;alpha <- 0.8
#' UtilAucCBM(mu,alpha)
#'
#'
#' @references
#' Dorfman DD, Berbaum KS (2000) A contaminated binormal model for ROC data: Part II.
#' A formal model, Acad Radiol 7:6 427--437.
#'
#'
#' @importFrom stats pnorm
#'
#' @export
#'
UtilAucCBM <- function (mu, alpha){
auc <- (1 - alpha) * 0.5 + alpha * pnorm(mu / sqrt(2))
return (auc)
}
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