wtd.var: Weighted Variance and Standard Deviation

In npreg: Nonparametric Regression via Smoothing Splines

Weighted Variance and Standard Deviation

Description

Generic function for calculating weighted variance or standard deviation of a vector.

Usage

wtd.var(x, weights, na.rm = FALSE)

wtd.sd(x, weights, na.rm = FALSE)

Arguments

x	Numerical or logical vector.
weights	Vector of non-negative weights.
na.rm	Logical indicating whether NA values should be removed before calculation.

Details

The weighted variance is defined as

(n / (n - 1)) * sum(weights * (x - xbar)^2) / sum(weights)

where n is the number of observations with non-zero weights, and xbar is the weighted mean computed via the wtd.mean function.

The weighted standard deviation is the square root of the weighted variance.

Value

Returns the weighted variance or standard deviation.

Note

If weights are missing, the weights are defined to be a vector of ones (which is the same as the unweighted variance or standard deviation).

Author(s)

Nathaniel E. Helwig <[e-mail]>

See Also

wtd.mean for weighted mean calculations

wtd.quantile for weighted quantile calculations

Examples

# generate data and weights
set.seed(1)
x <- rnorm(10)
w <- rpois(10, lambda = 10)

# weighted mean
xbar <- wtd.mean(x, w)

# weighted variance
wtd.var(x, w)
(10 / 9) * sum(w * (x - xbar)^2) / sum(w)

# weighted standard deviation
wtd.sd(x, w)
sqrt((10 / 9) * sum(w * (x - xbar)^2) / sum(w))

npreg documentation built on May 29, 2024, 4:17 a.m.