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

`ecdf(x)`# S3 method for ecdf
plot(x, …, ylab="Fn(x)", verticals = FALSE,
col.01line = "gray70", pch = 19)

# S3 method for ecdf
print(x, digits= getOption("digits") - 2, …)

# S3 method for ecdf
summary(object, …)
# S3 method for ecdf
quantile(x, …)

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`

.

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.

The e.c.d.f. (empirical cumulative distribution function) \(F_n\) 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`

\(= (\)\(x_1,x_2\), … \(x_n)\),
\(F_n\) is the fraction of observations less or equal to \(t\),
i.e.,
$$F_n(t) = \#\{x_i\le t\}\ / n
= \frac1 n\sum_{i=1}^n \mathbf{1}_{[x_i \le t]}.$$

The function `plot.ecdf`

which implements the `plot`

method for `ecdf`

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

; see its documentation.

`stepfun`

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

and `splinefun`

.

# NOT RUN { ##-- 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? 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) # }