#' Calculate weighted mean, var, sd with GIEMO
#'
#' @param d data vector
#'
#' @return list
#'
#' @export
#'
#' @examples
#' probs=runif(10)
#' weightedGIEMO(list(x = runif(10), p=(probs/sum(probs))))
#'
weightedGIEMO = function(d)
{
stopifnot(length(d$x)!=0)
stopifnot(is.numeric(d$x))
stopifnot(is.finite(d$x))
stopifnot(length(d$p)!=0)
stopifnot(is.numeric(d$p))
stopifnot(is.finite(d$p))
stopifnot(all.equal(sum(d$p),1))
mu = sum(d$x * d$p)
vari = sum(((d$x-mu)^2)*d$p)
sd = sqrt(vari)
list(mu = mu,vari = vari,sd = sd)
}
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