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```
#' Function compares nine deciles of stock return distributions.
#'
#' The first step computes a minimum reference return and nine deciles.
#' The input x must be a matrix having p columns (with a name for each column)
#' and n rows as in the data. If data are missing for some columns, insert NA's.
#' Thus x has p column of the data matrix ready for comparison and ranking.
#' For example, x has a matrix of stock returns.
#' The output matrix produced by this function also has p columns for each
#' column (i.e., for each stock being compared). The output matrix has
#' nineteen rows. The top nine rows have the magnitudes of deciles.
#' Rows 10 to 18 have respective ranks of the decile magnitudes.
#' The next (19-th) row of the output reports a weighted sum
#' of ranks.
#' Ranking always gives the smallest number 1 to the most desirable outcome.
#' We suggest that a higher portfolio weight
#' be given to the column having smallest rank value (along the 19th line).
#' The 20-th row further ranks the weighted sums of ranks in row 19. Investor
#' should choose the stock (column) representing the smallest rank
#' value along the last (20th) row of the `out' matrix.
#'
#' @param mtx { (n X p) matrix of data. For example, returns on p stocks n months}
#' @param howManySd {used to define `fixmin'= imaginary lowest return defined by going
#' howManySd=default=0.1 maximum of standard deviations of all stocks below
#' the minimum return for all stocks in the data}
### @importFrom moments skewness kurtosis
#' @return out is a matrix with p columns (same as in the input matrix) and
#' twenty rows. Top nine rows have 9 deciles, next nine rows have their ranks.
#' The 19-th row of `out' has a weighted sum of 9 ranks. All columns refer to
#' one stock. The weighted sum for each stock is then ranked. A
#' portfolio manager is assumed to prefer higher return represented by
#' high decile values represented by the column with the largest weighted sum.
#' can give largest weight to the column with the smallest bottom line.
#' The bottom line (20-th) labeled ``choice" of the `out' matrix is
#' defined so that choice =1 suggests the stock deserving
#' the highest weight in the portfolio. The portfolio manager will
#' generally give the lowest weight (=0?) to the stock representing column
#' having number p as the choice number. The manager may want to sell this stock.
#' Another output of the `decileVote' function is `fixmin' representing the
#' smallest possible return of all the stocks in the input `mtx' of returns.
#' It is useful as a reference stock. We compute stochastic dominance numbers
#' for each stock with this imaginary stock yielding fixmin return for all time
#' periods.
#'
### @note %% ~~further notes~~
#' @author Prof. H. D. Vinod, Economics Dept., Fordham University, NY
### @seealso \code{\link{}}
#' @examples
#' x1=c(1,4,7,2,6)
#' x2=c(3,4,8,4,7)
#' decileVote(cbind(x1,x2))
#'
#' @export
decileVote=function(mtx, howManySd=0.1){
n=NROW(mtx)
p=NCOL(mtx)
#compare deciles to zero return investment
pr=1:9/10
allmin=apply(mtx,2,min,na.rm=TRUE)
allsd=apply(mtx,2,sd,na.rm=TRUE)
maxsd=max(allsd,na.rm=TRUE)
fixmin=min(allmin,na.rm=TRUE)-howManySd*maxsd
# print(c("reference.min for all p columns",fixmin))
# q1=quantile(fixmin,probs=pr)
# print(q1)
#q1=rep(fixmin,p)
q2=apply(mtx,2,quantile,probs=pr,na.rm=TRUE)
# print(q1)
# print(q2)
decdiff=q2 #place to store
decRank=q2 #place to store
for (j in 1:p) {decdiff[,j]=q2[,j]-fixmin}
for (i in 1:9){decRank[i,]=(p+1)-rank(decdiff[i,],
na.last = TRUE, ties.method = "average")}
colsum=apply(decRank,2,sum)
ord1=rank(colsum,na.last=TRUE)
choice=ord1
out=rbind(q2,decRank,colsum,choice)
list(out=out,fixmin=fixmin)
}
```

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