Compute the median or quantiles a set of numbers which have weights associated with them.

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 NA values

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

## Value

A numeric vector.

## 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