Calculate central moments of distributions

This function calculates the \(n\)-th central moment, also known as the \(n\)-th moment about the mean, of a ddf distribution.

Usage

central_moment(dist, n)

Arguments

dist

A ddf object, the distribution.

n

An integer, the order of the moment.

Value

A double.

Details

The \(n\)-th central moment of a random variable \(X\) is given by $$E[(X - E[X])^n],$$ where \(E\) is the expectation operator.

See also

Other moments: moment(), standardized_moment()

Examples

# The zeroth central moment is always 1
central_moment(bin(5, 0.4), 0)
#> [1] 1

# The first central moment is always 0
central_moment(hypergeometric(10, 7, 5), n = 1)
#> [1] 0

# The second central moment is the variance
central_moment(unif(10), 2)
#> [1] 8.25
# Result using the formula for the uniform distribution
(10^2 - 1) / 12
#> [1] 8.25