R: Empirical Cumulative Distribution Function

ecdf {stepfun} | R Documentation

## Empirical Cumulative Distribution Function

### Description

Compute or plot an empirical cumulative distribution function.

### Usage

    ecdf(x)

    plot(..., verticals = FALSE, col.01line = "gray70")
    print(x, digits= getOption("digits") - 2, ...)
    summary(object, ...)

### Arguments

`x` | numeric vector of ``observations'' in `ecdf`; for the methods `x` is as `object` below.
`...` | arguments to be passed to `plot.stepfun`, the first of which should be an R object of class `"ecdf"`.
`verticals` | see `plot.stepfun`.
`col.01line` | numeric or character specifying the color of the horizontal lines at y=0 and 1, see `colors`.
`object` | (or `x`:) object of class `"ecdf"`, typically.
`digits` | number of significant digits to use, see `print`.

### Details

The e.c.d.f. (empirical cumulative distribution function) Fn is a step function with jump 1/n at each observation (possibly with multiple jumps at one place if there are ties).

For 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`; see its documentation.

### Value

For `ecdf`, a function 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  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))

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