| ecdf {stats} | R Documentation |
Compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an “ecdf” object.
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, ...)
x, object |
numeric vector of the observations for |
... |
arguments to be passed to subsequent methods, e.g.,
|
ylab |
label for the y-axis. |
verticals |
see |
col.01line |
numeric or character specifying the color of the
horizontal lines at y = 0 and 1, see |
pch |
plotting character. |
digits |
number of significant digits to use, see
|
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.,
Fn(t) = #{xi <= t}/n = 1/n sum(i=1,n) Indicator(xi <= t).
The function plot.ecdf which implements the plot
method for ecdf objects, is implemented via a call to
plot.stepfun; see its documentation.
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.
Martin Maechler, maechler@stat.math.ethz.ch.
Corrections by R-core.
stepfun, the more general class of step functions,
approxfun and splinefun.
##-- 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)