# ecdf {stats}

Empirical Cumulative Distribution Function
Package:
stats
Version:
R 3.0.2

### 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.

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

### 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)```

### Author(s)

Martin Maechler, maechler@stat.math.ethz.ch.
Corrections by R-core.

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