| % File src/library/stats/man/ecdf.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2019 R Core Team |
| % Copyright 2002-2016 The R Foundation |
| % Distributed under GPL 2 or later |
| |
| \name{ecdf} |
| \alias{ecdf} |
| \alias{plot.ecdf} |
| \alias{print.ecdf} |
| \alias{summary.ecdf} |
| \alias{quantile.ecdf} |
| \title{Empirical Cumulative Distribution Function} |
| \usage{ |
| ecdf(x) |
| |
| \method{plot}{ecdf}(x, \dots, ylab="Fn(x)", verticals = FALSE, |
| col.01line = "gray70", pch = 19) |
| |
| \method{print}{ecdf}(x, digits= getOption("digits") - 2, \dots) |
| |
| \method{summary}{ecdf}(object, \dots) |
| \method{quantile}{ecdf}(x, \dots) |
| } |
| \arguments{ |
| \item{x, object}{numeric vector of the observations for \code{ecdf}; for |
| the methods, an object inheriting from class \code{"ecdf"}.} |
| \item{\dots}{arguments to be passed to subsequent methods, e.g., |
| \code{\link{plot.stepfun}} for the \code{plot} method.} |
| \item{ylab}{label for the y-axis.} |
| \item{verticals}{see \code{\link{plot.stepfun}}.} |
| \item{col.01line}{numeric or character specifying the color of the |
| horizontal lines at y = 0 and 1, see \code{\link{colors}}.} |
| \item{pch}{plotting character.} |
| \item{digits}{number of significant digits to use, see |
| \code{\link{print}}.} |
| } |
| \description{ |
| Compute an empirical cumulative distribution function, with several |
| methods for plotting, printing and computing with such an |
| \dQuote{ecdf} object. |
| } |
| \details{ |
| The e.c.d.f. (empirical cumulative distribution function) |
| \eqn{F_n}{Fn} is a step function with jumps \eqn{i/n} at |
| observation values, where \eqn{i} is the number of tied observations |
| at that value. Missing values are ignored. |
| |
| For observations |
| \code{x}\eqn{= (}\eqn{x_1,x_2}{x1,x2}, \ldots \eqn{x_n)}{xn)}, |
| \eqn{F_n}{Fn} is the fraction of observations less or equal to \eqn{t}, |
| i.e., |
| \deqn{F_n(t) = \#\{x_i\le t\}\ / n |
| = \frac1 n\sum_{i=1}^n \mathbf{1}_{[x_i \le t]}.}{ |
| Fn(t) = #{xi <= t}/n = 1/n sum(i=1,n) Indicator(xi <= t).} |
| |
| The function \code{plot.ecdf} which implements the \code{\link{plot}} |
| method for \code{ecdf} objects, is implemented via a call to |
| \code{\link{plot.stepfun}}; see its documentation. |
| } |
| \value{ |
| For \code{ecdf}, a function of class \code{"ecdf"}, inheriting from the |
| \code{"\link{stepfun}"} class, and hence inheriting a |
| \code{\link{knots}()} method. |
| |
| For the \code{summary} method, a summary of the knots of \code{object} |
| with a \code{"header"} attribute. |
| |
| The \code{\link{quantile}(obj, ...)} method computes the same quantiles as |
| \code{quantile(x, ...)} would where \code{x} is the original sample. |
| } |
| \author{ |
| Martin Maechler; fixes and new features by other R-core members. |
| } |
| \note{ |
| The objects of class \code{"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 |
| \preformatted{ eval(attr(old_obj, "call"), environment(old_obj))} |
| since the data used is stored as part of the object's environment. |
| } |
| \seealso{\code{\link{stepfun}}, the more general class of step functions, |
| \code{\link{approxfun}} and \code{\link{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.out = 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) |
| } |
| \keyword{dplot} |
| \keyword{hplot} |