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.

### 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:
Fn <- ecdf(rnorm(12))
Fn
tt <- seq(-2,2, by = 0.1)
12* Fn(tt) # Fn is a `simple' function {with values k/12}
summary(Fn)
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(env= environment(Fn12)))
##[1] "f"  "method"  "n"  "x"  "y"  "yleft"  "yright"
utils::ls.str(environment(Fn12))

###----------------- 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) ; 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.h='red', add= TRUE)  #- plot method
abline(v=knots(Fn12),lty=2,col='gray70')
## luxury plot
plot(Fn12, verticals=TRUE, col.p='blue', col.h='red',col.v='bisque')

##-- this works too (automatic call to  ecdf(.)):
plot.ecdf(rnorm(24))
title("via  simple  plot.ecdf(x)", adj=1)

par(op)
```

[Package stats version 2.5.0 Index]