ecdf {stepfun}

R Documentation

Empirical Cumulative Distribution Function

Description

Compute or plot an empirical cumulative distribution function.

Usage

ecdf(x)

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

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))