\Header{ecdf}{Empirical Cumulative Distribution Function}
\alias{plot.ecdf}{ecdf}
\alias{print.ecdf}{ecdf}
\alias{summary.ecdf}{ecdf}
\keyword{dplot}{ecdf}
\keyword{hplot}{ecdf}
\begin{Description}\relax
Compute or plot an empirical cumulative distribution function.\end{Description}
\begin{Usage}
\begin{verbatim}
ecdf(x)

plot(..., verticals = FALSE, col.01line = "gray70")
print(x, digits= getOption("digits") - 2, ...)
summary(object, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] numeric vector of ``observations'' in \code{ecdf};  for the
methods \code{x} is as \code{object} below.
\item[\code{...}] arguments to be passed to \code{\Link{plot.stepfun}}, the
first of which should be an \R{} object of class \code{"ecdf"}.
\item[\code{verticals}] see \code{\Link{plot.stepfun}}.
\item[\code{col.01line}] numeric or character specifying the color of the
horizontal lines at y=0 and 1, see \code{\Link{colors}}.
\item[\code{object}] (or \code{x}:) object of class \code{"ecdf"}, typically.
\item[\code{digits}] number of significant digits to use, see \code{\Link{print}}.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The e.c.d.f. (empirical cumulative distribution function)
\eqn{F_n}{Fn} is a step
function with jump \eqn{1/n}{} at each observation (possibly with
multiple jumps at one place if there are ties).

For observations
\code{x}\eqn{= (}{}\eqn{x_1,x_2}{x1,x2}, \ldots \eqn{x_n)}{xn)},
\eqn{F_n}{Fn} is the fraction of observations less or equal to \eqn{t}{},
i.e.,
\deqn{F_n(t) = \#\{x_i\le t\}\ / n
= \frac1 n\sum_{i=1}^n \mathbf{1}_{[x_i \le t]}.}{Fn(t) = #\{x_i \le t\} / n  =  1/n sum(i=1,n) Indicator(xi <= t).}

The function \code{plot.ecdf} which implements the \code{\Link{plot}}
method for \code{ecdf} objects, is implemented via a call to
\code{\Link{plot.stepfun}}; see its documentation.\end{Details}
\begin{Value}
For \code{ecdf}, a function of class \code{"ecdf"}, inheriting from the
\code{"\Link{stepfun}"} class.\end{Value}
\begin{Author}\relax
Martin Maechler, \email{maechler@stat.math.ethz.ch}.\end{Author}
\begin{SeeAlso}\relax
\code{\Link{stepfun}}, the more general class of step functions,
\code{\Link{approxfun}} and \code{\Link{splinefun}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
##-- Simple didactical  ecdf  example:
Fn <- ecdf(rnorm(12))
Fn; summary(Fn)
12*Fn(knots(Fn)) == 1:12 ## == 1:12  if and only if there are no ties !

y <- round(rnorm(12),1); y[3] <- y[1]
Fn12 <- ecdf(y)
Fn12
print(knots(Fn12), dig=2)
12*Fn12(knots(Fn12)) ## ~= 1:12  if there where no ties

summary(Fn12)
summary.stepfun(Fn12)
print(ls.Fn12 <- ls(env= environment(Fn12)))
##[1] "f"  "method"  "n"  "ties"   "x"  "y"  "yleft"  "yright"

12 * Fn12((-20:20)/10)

###----------------- Plotting --------------------------

op <- par(mfrow=c(3,1), mgp=c(1.5, 0.8,0), mar= .1+c(3,3,2,1))

F10 <- ecdf(rnorm(10))
summary(F10)

plot(F10)
plot(F10, verticals= TRUE, do.p = FALSE)

plot(Fn12)# , lwd=2) dis-regarded
xx <- unique(sort(c(seq(-3,2, length=201), knots(Fn12))))
lines(xx, Fn12(xx), col='blue')
abline(v=knots(Fn12),lty=2,col='gray70')

plot(xx, Fn12(xx), type='b', cex=.1)#- plot.default
plot(Fn12, col.h='red', add= TRUE)  #- plot method
abline(v=knots(Fn12),lty=2,col='gray70')
plot(Fn12, verticals=TRUE, col.p='blue', col.h='red',col.v='bisque')
par(op)

##-- this works too (automatic call to  ecdf(.)):
plot.ecdf(rnorm(24))
\end{ExampleCode}
\end{Examples}

