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#' Probability function of Log-Logistics model
#' @param q input quantile for Log-Logistics model
#' @param shape shape parameter of Log-Logistics model
#' @param scale scale parameter of Log-Logistics model
#' @param lower.tail logic function to determine whether lower tail probability to be returned
#' @param log.p logic function to determine whether log of logistics to be returned
#' @return returns the probability of the Log-Logistics model
#' @examples
#' q <- c(1, 2, 3, 4)
#' # set paramters
#' shape <- 5
#' scale <- 3
#' log <- FALSE
#' result_1 <- marp::pllog(q, shape, scale, log)
#'
#' # alternatively, set log == TRUE
#' log <- TRUE
#' result_2 <- marp::pllog(q, shape, scale, log)
#'
#' @export
pllog <- function(q, shape = 1, scale = 1, lower.tail = TRUE, log.p = FALSE) {
Fx <- 1 / (1 + (q / scale) ^ { -shape})
if (!lower.tail)
Fx <- 1 - Fx
if (log.p)
Fx <- log(Fx)
return(Fx)
}
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