\HeaderA{sample}{Random Samples and Permutations}{sample}
\methaliasA{sample.int}{sample}{sample.int}
\keyword{distribution}{sample}
\begin{Description}\relax
\code{sample} takes a sample of the specified size from the elements
of \code{x} using either with or without replacement.
\end{Description}
\begin{Usage}
\begin{verbatim}
sample(x, size, replace = FALSE, prob = NULL)

sample.int(n, size, replace = FALSE, prob = NULL)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] Either a (numeric, complex, character or logical) vector of
more than one element from which to choose, or a positive integer.
\item[\code{n}] a non-negative integer, the number of items to choose from.
\item[\code{size}] positive integer giving the number of items to choose.
\item[\code{replace}] Should sampling be with replacement?
\item[\code{prob}] A vector of probability weights for obtaining the elements
of the vector being sampled.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
If \code{x} has length 1, is numeric (in the sense of
\code{\LinkA{is.numeric}{is.numeric}}) and \code{x >= 1}, sampling \emph{via}
\code{sample} takes place from
\code{1:x}.  \emph{Note} that this convenience feature may lead to
undesired behaviour when \code{x} is of varying length
\code{sample(x)}.  See the \code{resample()} example below.

By default \code{size} is equal to \code{length(x)}
so that \code{sample(x)} generates a random permutation
of the elements of \code{x} (or \code{1:x}).

The optional \code{prob} argument can be used to give a vector
of weights for obtaining the elements of the vector being
sampled. They need not sum to one, but they should be nonnegative
and not all zero.  If \code{replace} is true, Walker's alias method
(Ripley, 1987) is used when there are more than 250 reasonably
probable values: this gives results incompatible with those from \R{} \textless{}
2.2.0, and there will be a warning the first time this happens in a
session.

If \code{replace} is false, these probabilities are applied
sequentially, that is the probability of choosing the next item is
proportional to the weights amongst the remaining items.  The number
of nonzero weights must be at least \code{size} in this case.

\code{sample.int} is a bare interface in which both \code{n} and
\code{size} must be supplied as integers.
\end{Details}
\begin{Value}
For \code{sample} a vector of length \code{size} with elements
drawn from either \code{x} or from \code{1:x}.

For \code{sample.int}, an integer vector of length \code{size} with
elements from \code{1:n},
\end{Value}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.

Ripley, B. D. (1987) \emph{Stochastic Simulation}. Wiley.
\end{References}
\begin{SeeAlso}\relax
Package \pkg{sampling} for other methods of weighted sampling without
replacement.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
x <- 1:12
# a random permutation
sample(x)
# bootstrap sampling -- only if length(x) > 1 !
sample(x,replace=TRUE)

# 100 Bernoulli trials
sample(c(0,1), 100, replace = TRUE)

## More careful bootstrapping --  Consider this when using sample()
## programmatically (i.e., in your function or simulation)!

# sample()'s surprise -- example
x <- 1:10
    sample(x[x >  8]) # length 2
    sample(x[x >  9]) # oops -- length 10!
try(sample(x[x > 10]))# error!

## This is safer, but only for sampling without replacement
resample <- function(x, size, ...)
  if(length(x) <= 1) { if(!missing(size) && size == 0) x[FALSE] else x
  } else sample(x, size, ...)

resample(x[x >  8])# length 2
resample(x[x >  9])# length 1
resample(x[x > 10])# length 0
\end{ExampleCode}
\end{Examples}

