\Header{quantile}{Sample Quantiles}
\methalias{quantile.default}{quantile}
\keyword{univar}{quantile}
\begin{Description}\relax
The generic function \code{quantile} produces sample quantiles
corresponding to the given probabilities.
The smallest observation corresponds to a probability of 0 and the
largest to a probability of 1.\end{Description}
\begin{Usage}
\begin{verbatim}
quantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE, names = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] numeric vectors whose sample quantiles are wanted.
\item[\code{probs}] numeric vector with values in \eqn{[0,1]}{}.
\item[\code{na.rm}] logical; if true, any \code{\Link{NA}} and \code{NaN}'s
are removed from \code{x} before the quantiles are computed.
\item[\code{names}] logical; if true, the result has a \code{\Link{names}}
attribute.  Set to \code{FALSE} for speedup with many \code{probs}.

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
A vector of length \code{length(probs)} is returned;
if \code{names = TRUE}, it has a \code{\Link{names}} attribute.

\code{quantile(x,p)} as a function of \code{p} linearly interpolates
the points ( (i-1)/(n-1), ox[i] ), where
\code{ox <- order(x)} (the ``order statistics'') and \code{n <- length(x)}.

This gives \code{quantile(x, p) == (1-f)*ox[i] + f*ox[i+1]}, where
\code{r <- 1 + (n-1)*p}, \code{i <- floor(r)}, \code{f <- r - i}
\emph{and} \code{ox[n+1] :=  ox[n]}.

\code{\Link{NA}} and \code{\Link{NaN}} values in \code{probs} are
propagated to the result.\end{Details}
\begin{SeeAlso}\relax
\code{\Link{ecdf}} for empirical distributions of
\code{quantile} is  the "inverse".\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
quantile(x <- rnorm(1001))# Extremes & Quartiles by default
quantile(x,  probs=c(.1,.5,1,2,5,10,50, NA)/100)

n <- length(x) ## the following is exact, because 1/(1001-1) is exact:
stopifnot(sort(x) == quantile(x, probs = ((1:n)-1)/(n-1), names=F))

n <- 777
ox <- sort(x <- round(rnorm(n),1))# round() produces ties
ox <- c(ox, ox[n]) #- such that ox[n+1] := ox[n]
p <- c(0,1,runif(100))
i <- floor(r <- 1 + (n-1)*p)
f <- r - i
all(abs(quantile(x,p) - ((1-f)*ox[i] + f*ox[i+1])) < 20*.Machine$double.eps)
\end{ExampleCode}
\end{Examples}

