Compute the median, quantiles or variance of a set of numbers which have weights associated with them.
weighted.median(x, w, na.rm = TRUE, type=2, collapse=TRUE)weighted.quantile(x, w, probs=seq(0,1,0.25), na.rm = TRUE, type=4, collapse=TRUE)
weighted.var(x, w, na.rm = TRUE)
A numeric value or vector.
Data values. A vector of numeric values, for which the median or quantiles are required.
Weights.
A vector of nonnegative numbers, of the same length as x
.
Probabilities for which the quantiles should be computed. A numeric vector of values between 0 and 1.
Logical. Whether to ignore NA
values.
Integer specifying the rule for calculating the median or quantile,
corresponding to the rules available for
quantile
.
The only valid choices are type=1
, 2
or 4
.
See Details.
Research use only.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
The i
th 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
.
x <- 1:20
w <- runif(20)
weighted.median(x, w)
weighted.quantile(x, w)
weighted.var(x, w)
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