# [R] Confidence Band for empirical distribution function

kjetil brinchmann halvorsen kjetil at entelnet.bo
Mon Jul 21 23:23:14 CEST 2003

On 21 Jul 2003 at 15:42, Leif.Boysen wrote:

Here are some functions doing this using the package stepfun:

ecdf.ksCI <- function(x, main = NULL, sub = NULL,
xlab = deparse(substitute(x)), ...)
{
require(stepfun)
xlab
if(is.null(main))
main <- paste("ecdf(",deparse(substitute(x)),") + 95%
K.S.bands",
sep="")
n <- length(x)
if(is.null(sub))
sub <- paste("n = ", n)
ec <- ecdf(x)
xx <- get("x", envir=environment(ec))# = sort(x)
yy <- get("y", envir=environment(ec))
D <- approx.ksD(n)
yyu <- pmin(yy+D, 1)
yyl <- pmax(yy-D, 0)
ecu <- stepfun(xx, c(yyu, 1) )
ecl <- stepfun(xx, c(yyl, yyl[n]) )

## Plots -- all calling  plot.stepfun

plot(ec, main = main, sub = sub, xlab = xlab, ...)
col.hor="red" , col.vert="red", ...)
col.hor="red", col.vert="red", ...)
}

approx.ksD <- function(n)
{
## approximations for the critical level for Kolmogorov-Smirnov
## statistic D,
## for confidence level 0.95. Taken from Bickel & Doksum, table
IX,
## p.483
## and Lienert G.A.(1975) who attributes to Miller,L.H.(1956),
JASA
ifelse(n > 80,
1.358 /( sqrt(n) + .12 + .11/sqrt(n)),##Bickel&Doksum,
table
##IX,p.483

splinefun(c(1:9, 10, 15, 10 * 2:8),# from Lienert
c(.975,   .84189, .70760, .62394, .56328,# 1:5
.51926, .48342, .45427, .43001, .40925,# 6:10
.33760, .29408, .24170, .21012,# 15,20,30,40
.18841, .17231, .15975, .14960)) (n))
}

\name{ecdf.ksCI}
\alias{ecdf.ksCI}

\title{ Plotting the empirical distribution function together with
confidence
curves. }
\description{ Plots the empirical distribution function for one-
dimensional
data, together with upper and lower confidence curves. Always
uses
pointwise confidence level of 95\%.

}
\usage{
ecdf.ksCI(x, main=NULL, sub=NULL, xlab = deparse(substitute(x)), ...)
}
%- maybe also usage' for other objects documented here.
\arguments{
\item{x}{ \code{x} numerical vector of observations.  }
\item{\dots}{ \code{\dots} arguments given to
}
\details{
}
\value{
Nothing. Used for its side effect, to produce a plot.
}
\references{ Peter J. Bickel & Kjell A. Doksum: Mathematical
Statistics, Basic Ideas and Selected
Topics. Holden-Day, 1977. }
\author{ Kjetil Halvorsen }

package

\examples{
ecdf.ksCI( rchisq(50,3) )
}
\keyword{ hplot }
\keyword{nonparametric}

Kjetil Halvorsen

> Hi,
>
> I was trying to draw an empirical distribution function with uniform
> confidence bands. So I tried to find a way to calculate values of the
> Kolmogorov-Smirnov Distribution but failed.
> I guess it must be hidden somewhere (since the ks-test is implemented),
> but I was unable to find it.
>
> Is there any way to do this?
>
> Thanks
>
> Leif Boysen
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

`