| 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 vector whose sample quantiles are wanted, or an
object of a class for which a method has been defined (see also
‘details’). NA and NaN values are not
allowed in numeric vectors unless na.rm is TRUE. |
probs |
numeric vector of probabilities with values in [0,1]. (As from R 2.8.0 values up to 2e-14 outside that range are accepted and moved to the nearby endpoint. |
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.
The default method works with 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.
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.
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 - γ) x[j] + γ 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, the value of γ 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.
Continuous sample quantile types 4 through 9
For types 4 through 9, Q[i](p) is a continuous function of p, with gamma = g and m given below. The sample quantiles can be obtained equivalently by linear interpolation between the points (p[k],x[k]) where x[k] is the kth order statistic. Specific expressions for p[k] are given below.
x.
x is normally distributed.
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 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)