Summary Moments: Mean, Variance, Skewness and Kurtosis

Usage

bd_moment_summary(a, b, c, k, rel.tol = 1e-10, subdivisions = 4000L)

Arguments

a: Shape parameter (beta generator).
b: Shape parameter governing the tail.
c: Shape parameter (baseline).
k: Scale parameter (baseline).
rel.tol: Relative accuracy, passed to [stats::integrate()].
subdivisions: Subdivision limit, passed to [stats::integrate()].

Value

A named numeric vector. Entries requiring a moment that does not exist are `NA`, with the governing condition given in the `condition` attribute.

Details

Skewness needs \(b > 3\) and kurtosis \(b > 4\). Both are frequently unavailable for fitted values of \(b\), which is a property of the family rather than a limitation of the computation.

Examples

bd_moment_summary(a = 1.5, b = 5, c = 2, k = 1)
#>       mean   variance         sd   skewness   kurtosis 
#>  1.0517578  0.7961493  0.8922720  3.6708237 49.3171010 
#> attr(,"condition")
#> [1] "E(Z^r) is finite if and only if b > r"
bd_moment_summary(a = 1.5, b = 2.5, c = 2, k = 1)   # skew/kurt unavailable
#>      mean  variance        sd  skewness  kurtosis 
#>  2.358122 16.304237  4.037851        NA        NA 
#> attr(,"condition")
#> [1] "E(Z^r) is finite if and only if b > r"