| ecdf {stats} | R Documentation |
Compute or plot an empirical cumulative distribution function.
ecdf(x)
## S3 method for class 'ecdf':
plot(x, ..., ylab="Fn(x)", verticals = FALSE,
col.01line = "gray70")
## S3 method for class 'ecdf':
print(x, digits= getOption("digits") - 2, ...)
x |
numeric vector of “observations” in ecdf; for
the methods, an object of class "ecdf", typically. |
... |
arguments to be passed to subsequent methods, i.e.,
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. |
digits |
number of significant digits to use, see
print. |
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) = #{x_i <= 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.
Prior to R 2.1.0, ecdf treated ties differently, so had
multiple jumps of size 1/n at tied observations. This was not
the most common definition, and could be very slow for large datasets
with many ties.
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: 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 were no ties summary(Fn12) summary.stepfun(Fn12) print(ls.Fn12 <- ls(env= environment(Fn12))) ##[1] "f" "method" "n" "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))