# ecdf {stats}

### Description

Compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an “ecdf” object.

### Usage

ecdf(x) ## S3 method for class 'ecdf': plot((x, ..., ylab="Fn(x)", verticals = FALSE, col.01line = "gray70", pch = 19)) ## S3 method for class 'ecdf': print((x, digits= getOption("digits") - 2, ...)) ## S3 method for class 'ecdf': summary((object, ...)) ## S3 method for class 'ecdf': quantile((x, ...))

### Arguments

- x, object
- numeric vector of the observations for
`ecdf`

; for the methods, an object inheriting from class`"ecdf"`

. - ...
- arguments to be passed to subsequent methods, e.g.,
`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`

. - pch
- plotting character.
- 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 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.,

The function `plot.ecdf`

which implements the `plot`

method for `ecdf`

objects, is implemented via a call to `plot.stepfun`

; see its documentation.

### Values

For `ecdf`

, a function of class `"ecdf"`

, inheriting from the `"stepfun"`

class, and hence inheriting a `knots()`

method.

For the `summary`

method, a summary of the knots of `object`

with a `"header"`

attribute.

The `quantile(obj, ...)`

method computes the same quantiles as `quantile(x, ...)`

would where `x`

is the original sample.

### Examples

##-- Simple didactical ecdf example : x <- rnorm(12) Fn <- ecdf(x) Fn # a *function* Fn(x) # returns the percentiles for x tt <- seq(-2, 2, by = 0.1) 12 * Fn(tt) # Fn is a 'simple' function {with values k/12} summary(Fn) ##--> see below for graphics knots(Fn) # the unique data values {12 of them if there were no ties} y <- round(rnorm(12), 1); y[3] <- y[1] Fn12 <- ecdf(y) Fn12 knots(Fn12) # unique values (always less than 12!) summary(Fn12) summary.stepfun(Fn12) ## Advanced: What's inside the function closure? print(ls.Fn12 <- ls(environment(Fn12))) ##[1] "f" "method" "n" "x" "y" "yleft" "yright" utils::ls.str(environment(Fn12)) stopifnot(all.equal(quantile(Fn12), quantile(y))) ###----------------- Plotting -------------------------- require(graphics) 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.points = FALSE) plot(Fn12 , lwd = 2) ; mtext("lwd = 2", adj = 1) 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 = "o", cex = .1) #- plot.default {ugly} plot(Fn12, col.hor = "red", add = TRUE) #- plot method abline(v = knots(Fn12), lty = 2, col = "gray70") ## luxury plot plot(Fn12, verticals = TRUE, col.points = "blue", col.hor = "red", col.vert = "bisque") ##-- this works too (automatic call to ecdf(.)): plot.ecdf(rnorm(24)) title("via simple plot.ecdf(x)", adj = 1) par(op)

Documentation reproduced from R 3.0.2. License: GPL-2.