R/seq_fwd_nexp_mean.R

In yelleKneK/SMSD: Sequential Methods for Study Design

#' seq_fwd_nexp_mean
#'
#' Purely Sequential approach to Get Fixed Width Confidence Interval
#' for the mean of negative exponential random variables.
#'
#' @param data The data for which to calculate the confidence interval.
#' A numeric vector.
#' @param d Half of the confidence interval width, must be a non-zero positive
#' value.
#' @param alpha The significance level. A value between 0 and 1.
#' @param gamma gamma
#' @param pilot Should a pilot sample be generated. TRUE/FALSE value.
#' default value is \code{FALSE}.
#' @param verbose Should the criterion be printed. Default is \code{FALSE}.
#' @param na.rm This parameter controls whether NA values are removed from
#' the data prior to calculation. Default is \code{TRUE}.
#'
#' @return The calculated confidence interval, the sample size, data mean,
#' and an indicator of if the criterion was satisfied.
#'
#' @author Bhargab Chattopadhyay \email{Bhargab@iiitvadodara.ac.in},
#' Neetu Shah \email{201451015@iiitvadodara.ac.in}, Ken Kelley \email{kkelley@nd.edu}
#'
#' @references
#' Mukhopadhyay, N., \& de Silva, Basil M. (2009). \emph{Sequential Methods and Their Applications}. New York: CRC Press.
#'
#'
#' @export seq_fwd_nexp_mean
#'
#'
#' @examples
#' pilot_ss <- seq_fwd_nexp_mean(alpha=0.05, d=0.2, gamma=1, pilot=TRUE)
#' SLS <- rexp(pilot_ss, rate=1)
#' seq_fwd_nexp_mean(data=SLS, d=0.2, alpha=0.05, pilot=FALSE)
seq_fwd_nexp_mean <- function(data, d, alpha, gamma,
                              pilot=FALSE, verbose=FALSE, na.rm=TRUE){
  if(missing(d)){
    stop("You must specify \'d\'")
  }

  if(missing(alpha)){
    stop("You must specify \'alpha\'")
  }

  if(!missing(d)){
    if(d<0) stop("d should be a non-zero positive value")
  }

  if(!missing(alpha)){
    if(alpha>1 & alpha<0) stop("alpha should be between 0 and 1")
  }

  if(missing(gamma)) gamma <- 1

  if(pilot==FALSE)
  {
    if (!is.data.frame(data) && !is.matrix(data) && !is.vector(data)){
      stop("The argument 'data' must be a data.frame
           or matrix with one column")
    }

    if (dim(data)[2] != 1 && !is.null(data) && !is.vector(data)){
      stop("The argument 'data' must have only one column,
           or be 'NULL' for pilot = TRUE")
    }


    if(is.data.frame(data))
    {
      data <- as.vector(data)
    }
    if(na.rm){
      data <-  data[!is.na( data)]
    }
    n <- length(data)

    U <- sum(data-min(data))/(n-1)

    optimal_N <- as.integer(((-log(alpha, base = exp(1)))/d)*U)

    ci <- c(min(data)-d, min(data))

    if(verbose==FALSE){
      Outcome <- list("Confidence Interval"=ci[1],ci[2],
                            N=n, mean=mean(data),
                            "Is.Satisfied?"=(n >= optimal_N))
    }
    if(verbose==TRUE) {
      Outcome <- list("Confidence Interval"=ci[1],ci[2],
                            N=n, mean=mean(data),
                            Criterion=optimal_N,
                           "Is.Satisfied?"= (n >= optimal_N))
      }
  }

  if(pilot==TRUE) {
    Outcome <- c(Pilot.SS=max(2,
                              ceiling((stats::qnorm(1-alpha)/d)^(2/(1+gamma)))
                              +1))
  }

  return(Outcome)
}