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.
quantile(x, ...)
"quantile"(x, probs = seq(0, 1, 0.25), na.rm = FALSE, names = TRUE, type = 7, ...)NA and NaN values are not
allowed in numeric vectors unless na.rm is TRUE.NA and NaN's
are removed from x before the quantiles are computed.names
attribute. Set to FALSE for speedup with many probs.quantile returns estimates of underlying distribution quantiles
based on one or two order statistics from the supplied elements in
x at probabilities in probs. One of the nine quantile
algorithms discussed in Hyndman and Fan (1996), selected by
type, is employed. All sample quantiles are defined as weighted averages of
consecutive order statistics. Sample quantiles of type $i$
are defined by:
$$Q_{i}(p) = (1 - \gamma)x_{j} + \gamma x_{j+1}$$
where $1 \le i \le 9$,
$(j-m)/n \le p < (j-m+1)/n$,
$x[j]$ is the $j$th order statistic, $n$ is the
sample size, the value of $\gamma$ is a function of
$j = floor(np + m)$ and $g = np + m - j$,
and $m$ is a constant determined by the sample quantile type. Discontinuous sample quantile types 1, 2, and 3 For types 1, 2 and 3, $Q[i](p)$ is a discontinuous
function of $p$, with $m = 0$ when $i = 1$ and $i =
2$, and $m = -1/2$ when $i = 3$. x.
x is normally distributed.
length(probs) is returned;
if names = TRUE, it has a names attribute. NA and NaN values in probs are
propagated to the result.
The default method works with classed objects sufficiently like
numeric vectors that sort and (not needed by types 1 and 3)
addition of elements and multiplication by a number work correctly.
Note that as this is in a namespace, the copy of sort in
base will be used, not some S4 generic of that name. Also note
that that is no check on the ‘correctly’, and so
e.g. quantile can be applied to complex vectors which (apart
from ties) will be ordered on their real parts.
There is a method for the date-time classes (see
"POSIXt"). Types 1 and 3 can be used for class
"Date" and for ordered factors.
Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical packages, American Statistician 50, 361--365.
ecdf for empirical distributions of which
quantile is an inverse;
boxplot.stats and fivenum for computing
other versions of quartiles, etc.
quantile(x <- rnorm(1001)) # Extremes & Quartiles by default
quantile(x, probs = c(0.1, 0.5, 1, 2, 5, 10, 50, NA)/100)
### Compare different types
p <- c(0.1, 0.5, 1, 2, 5, 10, 50)/100
res <- matrix(as.numeric(NA), 9, 7)
for(type in 1:9) res[type, ] <- y <- quantile(x, p, type = type)
dimnames(res) <- list(1:9, names(y))
round(res, 3)
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