Moments of a Distribution

Get common moment-related quantities of a distribution: mean, variance, standard deviation (stdev), skewness, and kurtosis or excess kurtosis (kurtosis_exc). If these quantities are not supplied in the distribution's definition, a numerical algorithm may be used.

Usage

kurtosis(distribution)

kurtosis_exc(distribution)

# S3 method for class 'dst'
mean(x, ...)

skewness(distribution)

stdev(distribution)

variance(distribution)

Arguments

x, distribution

Distribution to evaluate.

...

When calculating the mean via integration of the quantile function, arguments passed to stats::integrate().

Value

A single numeric.

Details

If a moment is not supplied in the distribution's definition, it is computed numerically over the distribution's support: a sum over the atoms (the discrete part) plus integration of the density over the continuous part. An infinite atomic support (such as a Poisson's) is summed by walking outward through its atoms until the tail contribution is negligible.

Note

When a moment is computed numerically and the underlying sum or integral does not converge — for example, a heavy-tailed distribution whose moment is not finite — the result is NaN.

Examples

a <- dst_gp(1, 0.5)
b <- dst_unif(0, 1)
c <- dst_norm(3, 4)
mean(a)
#> [1] 2
variance(b)
#> [1] 0.08333333
kurtosis(c)
#> [1] 3
kurtosis_exc(c)
#> [1] 0