R: Empirical Cumulative Distribution Function

ecdf {stats} | R Documentation

## Empirical Cumulative Distribution Function

### Description

Compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an “ecdf” object.

### 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, ...)
    ## S3 method for class 'ecdf'
    quantile(x, ...)

### 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) 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.

### Value

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.

### Note

The objects of class `"ecdf"` are not intended to be used for permanent storage and may change structure between versions of R (and did at R 3.0.0). They can usually be re-created by

        eval(attr(old_obj, "call"), environment(old_obj))

since the data used is stored as part of the object's environment.

### Author(s)

Martin Maechler; fixes and new features by other R-core members.

### 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?
    ls(environment(Fn12))
    ## "f"     "method" "na.rm"  "nobs"   "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)

[Package stats version 4.0.5 Index]