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")

## S3 method for class 'ecdf':
print(x, digits= getOption("digits") - 2, ...)
```

### Arguments

 `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`.

### Details

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.

### Value

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

### Warning

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.

### Author(s)

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

`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 <- y
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)))
## "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))
```

[Package stats version 2.1.0 Index]