ecdf {stats}

R Documentation

Empirical Cumulative Distribution Function

Description

Compute or plot an empirical cumulative distribution function.

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, ...)

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) 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.

Value

For ecdf, a function of class "ecdf", inheriting from the "stepfun" class.

For the summary method, a summary of the knots of object with a "header" attribute.

Author(s)

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

See Also

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))


###----------------- 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)

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