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#' Creates input for the stochastic dominance function stochdom2
#'
#' Stochastic dominance is a sophisticated comparison of two distributions of
#' stock market returns. The dominating distribution is superior in terms of
#' mean, variance, skewness and kurtosis respectively, representing dominance
#' orders 1 to 4, without directly computing four moments. Vinod(2008) sec. 4.3
#' explains the details. The `wtdpapb' function creates the input
#' for stochdom2 which in turn computes the stochastic dominance.
#' See Vinod (2004) for details about quantitative stochastic dominance.
#'
#' @note Function is needed before using stochastic dominance
#'
#' @param xa {Vector of (excess) returns for the first investment option A or
#' values of any random variable being compared to another.}
#' @param xb Vector of returns for the second option B
#' @return
#' \item{wpa}{Weighted vector of probabilities for option A}
#' \item{wpb}{Weighted vector of probabilities for option B}
#' \item{dj}{Vector of interval widths (distances) when both sets of data are forced on a common support}
#' @note In Vinod (2008) where the purpose of \code{wtdpapb} is to map from standard
#' `expected utility theory' weights to more sophisticated `non-expected utility
#' theory' weights using Prelec's (1998, Econometrica, p. 497) method. These
#' weights are not needed here. Hence we provide the function \code{prelec2}
#' which does not use Prelec weights at all, thereby simplifying and speeding up
#' the R code provided in Vinod (2008). This function avoids sophisticated `non-expected'
#' utility theory which incorporates commonly observed human behavior favoring
#' loss aversion and other anomalies inconsistent with precepts of the
#' expected utility theory. Such weighting is not needed for our application.
#' @author Prof. H. D. Vinod, Economics Dept., Fordham University, NY
#' @seealso See Also \code{\link{stochdom2}}
#' @references Vinod, H. D.', 'Hands-On Intermediate Econometrics
#' Using R' (2008) World Scientific Publishers: Hackensack, NJ.
#' \url{https://www.worldscientific.com/worldscibooks/10.1142/12831}
#'
#' @references Vinod, H. D. 'Ranking Mutual Funds Using
#' Unconventional Utility Theory and Stochastic Dominance,'
#' Journal of Empirical Finance Vol. 11(3) 2004, pp. 353-377.
#'
#' @concept stochastic dominance
#' @examples
#'
#' \dontrun{
#' set.seed(234);x=sample(1:30);y=sample(5:34)
#' wtdpapb(x,y)}
#'
#' @export
wtdpapb <- function(xa, xb) {
# input: excess returns for mutual fund A & B output is a weighted pa and pb
# vectors (wpa, wpb) and dj vector
Ta = length(xa)
Tb = length(xb)
k = Ta + Tb
pa0 = rep(1/Ta, Ta)
pb0 = rep(1/Tb, Tb)
xpapb = matrix(0, k, 3)
for (i in 1:Ta) {
xpapb[i, 1] = xa[i]
xpapb[i, 2] = pa0[i]
}
for (i in 1:Tb) {
xpapb[Ta + i, 1] = xb[i]
xpapb[Ta + i, 3] = pb0[i]
}
pra = prelec2(n = Ta + Tb)
sm = sort_matrix(xpapb, 1) #sort on first col of excess returns
pa = sm[, 2]
pb = sm[, 3]
wpa = pa * pra$pdif
wpb = pb * pra$pdif
dj=sm[,1]-sm[1,1] #deviations from the minimum
#at sm[1,1] (sm is sorted)
list(wpa = wpa, wpb = wpb, dj = dj)
}
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