Compute the median or quantiles a set of numbers which have weights associated with them.
Usage
weighted.median(x, w, na.rm = TRUE, type = 2)
weighted.quantile(x, w, probs = seq(0, 1, 0.25), na.rm = TRUE, type = 4)Source
These functions are adapted from their homonyms developed by Adrian
Baddeley in the spatstat package.
Arguments
- x
a numeric vector of values
- w
a numeric vector of weights
- na.rm
a logical indicating whether to ignore
NAvalues- type
Integer specifying the rule for calculating the median or quantile, corresponding to the rules available for
stats:quantile(). The only valid choices are type=1, 2 or 4. See Details.- probs
probabilities for which the quantiles should be computed, a numeric vector of values between 0 and 1
Details
The ith observation x[i] is treated as having a weight proportional to
w[i].
The weighted median is a value m such that the total weight of data less
than or equal to m is equal to half the total weight. More generally, the
weighted quantile with probability p is a value q such that the total
weight of data less than or equal to q is equal to p times the total
weight.
If there is no such value, then
if
type = 1, the next largest value is returned (this is the right-continuous inverse of the left-continuous cumulative distribution function);if
type = 2, the average of the two surrounding values is returned (the average of the right-continuous and left-continuous inverses);if
type = 4, linear interpolation is performed.
Note that the default rule for weighted.median() is type = 2, consistent
with the traditional definition of the median, while the default for
weighted.quantile() is type = 4.
Examples
x <- 1:20
w <- runif(20)
weighted.median(x, w)
#> [1] 9.5
weighted.quantile(x, w)
#> 0% 25% 50% 75% 100%
#> 1.000000 4.656370 9.511679 16.012960 20.000000