#' seq_mr_dfr_mean
#'
#' @description Purely Sequential approach to Get Minimum Risk Point Estimation
#' for distribution free random variables with known variance
#'
#' @param data The data for which to calculate the minimum risk point.
#' @param A The loss function constant.
#' @param c The cost of unit sample.
#' @param lowerlim The lower bound for the variance.
#' @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 risk, the sample size, mean, standard deviation, 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_mr_dfr_mean
#'
#' @examples
#' pilot_ss <- seq_mr_dfr_mean(A=100, c=2, pilot=TRUE)
#' SLS <- rnorm(pilot_ss, mean=0, sd=1)
#' seq_mr_dfr_mean(data=SLS, A=100, c=2, lowerlim=2, pilot=FALSE)
seq_mr_dfr_mean <- function(data, A, c, lowerlim ,
pilot=FALSE, verbose=FALSE,
na.rm=TRUE){
if(!missing(A))
{
if(A<=0) stop("A should be a non-zero positive value")
}
if(missing(A)){
stop("You must specify \'A\'")
}
if(!missing(c))
{
if(c<=0) stop("c should be a non-zero positive value")
}
if(missing(c)){
stop("You must specify \'c\'")
}
if(pilot==FALSE)
{
if(!missing(lowerlim))
{
if(lowerlim<=0){
stop("c should be a non-zero positive value")
}
}
if(missing(lowerlim)){
stop("You must specify \'lower bound\'")
}
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 <- max(length(data), ceiling(sqrt((A/c)*lowerlim)))
optimal_N <- as.integer(sqrt((A/c)*stats::var(data)))
Rk<-(1/n)*A*stats::var(data)+(c*n)
if(verbose==FALSE){
Outcome <- rbind(list(Risk=Rk, N=length(data),
mean=mean(data),
"Is.Satisfied?"=(n >= optimal_N)))
}
if(verbose==TRUE){
Outcome <- rbind(list(Risk=Rk, N=length(data),
mean=mean(data),
Criterion=optimal_N,
Is.Satisfied=n >= optimal_N))
}
}
if(pilot==TRUE){
Outcome <- c(Pilot.SS=max(4, ceiling((A/c)^(1/2))))
}
return(Outcome)
}
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