\name{ewcdf}
\alias{ewcdf}
\title{Weighted Empirical Cumulative Distribution Function}
\description{
  Compute a weighted version of the
  empirical cumulative distribution function.
}
\usage{
ewcdf(x, weights = rep(1/length(x), length(x)))
}
\arguments{
  \item{x}{Numeric vector of observations.}
  \item{weights}{Numeric vector of non-negative weights
    for \code{x}.}
}
\details{
  This is a modification of the standard function \code{\link{ecdf}}
  allowing the observations \code{x} to have weights.

  The weighted e.c.d.f. (empirical cumulative distribution function)
  \code{Fn} is defined so that, for any real number \code{y}, the value of
  \code{Fn(y)} is equal to the total weight of all entries of
  \code{x} that are less than or equal to \code{y}. That is
  \code{Fn(y) = sum(weights[x <= y])}.

  Thus \code{Fn} is a step function which jumps at the
  values of \code{x}. The height of the jump at a point \code{y}
  is the total weight of all entries in \code{x} 
  number of tied observations at that value.  Missing values are
  ignored.

  If \code{weights} is omitted, the default is equivalent to
  \code{ecdf(x)}.
}
\value{
  A function, of class \code{"ecdf"}, inheriting from \code{"stepfun"}.
}
\author{Adrian Baddeley
  \email{adrian@maths.uwa.edu.au}
  \url{http://www.maths.uwa.edu.au/~adrian/}
  and Rolf Turner
  \email{r.turner@auckland.ac.nz}
}
\seealso{
  \code{\link{ecdf}}
}
\examples{
   x <- rnorm(100)
   w <- runif(100)
   plot(ewcdf(x,w))
}
\keyword{nonparametric}
\keyword{univar}