ecdf {stats} | R Documentation |

Compute or plot an empirical cumulative distribution function.

ecdf(x) ## S3 method for class 'ecdf': plot(x, ..., ylab="Fn(x)", verticals = FALSE, col.01line = "gray70") ## S3 method for class 'ecdf': print(x, digits= getOption("digits") - 2, ...)

`x` |
numeric vector of “observations” in `ecdf` ; for
the methods, an object of class `"ecdf"` , typically. |

`...` |
arguments to be passed to subsequent methods, i.e.,
`plot.stepfun` for the `plot` method. |

`ylab` |
label for the y-axis. |

`verticals` |
see `plot.stepfun` . |

`col.01line` |
numeric or character specifying the color of the
horizontal lines at y = 0 and 1, see `colors` . |

`digits` |
number of significant digits to use, see
`print` . |

The e.c.d.f. (empirical cumulative distribution function)
*Fn* is a step function with jumps *i/n* at
observation values, where *i* is the number of tied observations
at that value. Missing values are ignored.

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.

For `ecdf`

, a function of class `"ecdf"`

, inheriting from the
`"stepfun"`

class.

Prior to **R** 2.1.0, `ecdf`

treated ties differently, so had
multiple jumps of size *1/n* at tied observations. This was not
the most common definition, and could be very slow for large datasets
with many ties.

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

Corrections by R-core.

`stepfun`

, the more general class of step functions,
`approxfun`

and `splinefun`

.

##-- 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 were 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 = 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))

[Package *stats* version 2.2.1 Index]