

   EEmmppiirriiccaall CCuummuullaattiivvee DDiissttrriibbuuttiioonn FFuunnccttiioonn

        ecdf(x)
        plot(ecdf(x), verticals = FALSE, col.01line = "gray70", ...)

   AArrgguummeennttss::

          x: numeric vector with the ``observations''.

   DDeessccrriippttiioonn::

        For observations `x', `ecdf(x)' returns the e.c.d.f.
        (empirical cumulative distribution function), i.e.  the
        function Fn.  Given  the observations, `x'=
        (x1,x2,...xn), Fn is the fraction of observations less
        or equal to t, i.e.,

        Fn(t) = #{x_i <= t} / n  =  1/n sum(i=1,..,n) Indicator(xi <= t).

        The function `plot.ecdf' which implements the `plot'
        method for `ecdf' objects, is implemented via a call to
        `plot.stepfun'.

   VVaalluuee::

        An R function Fn of class `"ecdf"', inheriting from the
        `"stepfun"' class.

   AAuutthhoorr((ss))::

        Martin Maechler, maechler@stat.math.ethz.ch.

   SSeeee AAllssoo::

        `stepfun', the more general class of step functions,
        `approxfun' and `splinefun'.

   EExxaammpplleess::

        ##-- Simple didactical  ecdf  example:
        Fn <- ecdf(rnorm(12))
        Fn; summary(Fn)
        12*Fn(knots(Fn)) == 1:12 ## == 1:12  iff 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"      "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 = F)

        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=T, col.p='blue', col.h='red',col.v='bisque')
        par(op)

        ##-- this works too (automatic call to  ecdf(.)):
        plot.ecdf(rnorm(24))

