## Empirical Cumulative Distribution Function

## Usage

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

## Arguments

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

## Description

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`.

## Value

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

## Author(s)

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

## See Also

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

## Examples

    ##-- 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))

[Package Contents]