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#' @title Generates parameters for the beta distribution # I don't think we need to show this as a separate function,
#' but put together with gen.eff.stg1 or be called by gen.eff.stg1
#'
#' @description Function \code{beta.ab()} returns parameters alpha and beta for generating beta r.v. (per dose)
#'
#' @return Vector of alpha and beta values for generating beta random variable for a dose.
#'
#' @param m mean efficacies for given dose. Values range from 0 - 100. (e.g, T cell persistence - values b/w 5 and 80 per cent)
#' @param v efficacy variance per dose. Values range from 0 - 1. (e.g., 0.01)
#'
#' @export
#'
#' @keywords internal
beta.ab <- function(m, v) {
a <- seq(0.5, 20, 0.01) # a is a seq of alpha in beta distr.
b <- a * (1 - m) / m
vfit <- a * b / ((a + b + 1) * (a + b)^2)
diff <- abs(vfit - v)
index <- (1:length(diff))[diff == min(diff)] # return the index of the min var.
return(list(a = a[index],
b = b[index])) # return alpha and beta for the min.var.
}
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