quantile {stats} | R Documentation |
The generic function 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, ...) ## Default S3 method: quantile(x, probs = seq(0, 1, 0.25), na.rm = FALSE, names = TRUE, type = 7, ...)
x |
numeric vectors whose sample quantiles are wanted. Missing values are ignored. |
probs |
numeric vector of probabilities with values in [0,1]. |
na.rm |
logical; if true, any NA and NaN 's
are removed from x before the quantiles are computed. |
names |
logical; if true, the result has a names
attribute. Set to FALSE for speedup with many probs . |
type |
an integer between 1 and 9 selecting one of the nine quantile algorithms detailed below to be used. |
... |
further arguments passed to or from other methods. |
A vector of length length(probs)
is returned;
if names = TRUE
, it has a names
attribute.
NA
and NaN
values in probs
are
propagated to the result.
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.
Sample quantiles of type i are defined by
Q[i](p) = (1 - gamma) x[j] + gamma x[j+1],
where 1 <= i <= 9, (j-m)/n <= p < (j-m+1)/ n, x[j] is the jth order statistic, n is the sample size, and m is a constant determined by the sample quantile type. Here gamma depends on the fractional part of g = np+m-j.
For the continuous sample quantile types (4 through 9), the sample quantiles can be obtained by linear interpolation between the kth order statistic and p(k):
p(k) = (k - alpha) / (n - alpha - beta + 1),
where α and β are constants determined by the type. Further, m = alpha + p(1 - alpha - beta), and gamma = g.
Discontinuous sample quantile types 1, 2, and 3
Continuous sample quantile types 4 through 9
x
.
x
is normally distributed.
Hyndman and Fan (1996) recommend type 8. The default method is type 7, as used by S and by R < 2.0.0.
of the version used in R >= 2.0.0, Ivan Frohne and Rob J Hyndman.
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
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 the “inverse”;
boxplot.stats
and fivenum
for computing
“versions” of quartiles, etc.
quantile(x <- rnorm(1001))# Extremes & Quartiles by default quantile(x, probs=c(.1,.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)