uMpool {Umoments}R Documentation

Pooled central moment estimates - two-sample

Description

Calculate unbiased pooled estimates of central moments and their powers and products up to specified order.

Usage

uMpool(smp, a, order)

Arguments

smp

sample.

a

vector of the same length as smp specifying categories of observations (should contain two unique values).

order

highest order of the estimates to calclulate. Estimates of lower orders will be included.

Details

Pooled estimates up to the 6th order can be calculated. Second and third orders contain estimates of the variance and third central moment, fourth order includes estimates of fourth moment and squared variance (μ22\mu_2^2), fifth order - of fifth moment and a product of second and third moments (μ2μ3\mu_2 \mu_3), sixth order - of sixth moment, a product of second and fourth moments (μ2μ4\mu_2 \mu_4), squared third moment (μ32\mu_3^2), and cubed variance (μ23\mu_2^3).

Value

A named vector of estimates of central moments and their powers and products up to order. The highest order available is 6th. The names of the elements are "M2", "M3", "M4", "M5", "M6" for corresponding central moments, "M2M3", "M2M4" for products of the moments (second and third, second and fourth), and "M2pow2", "M2pow3", "M3pow2" for powers of the moments - corresponding to estimates of squared variance, cubed variance, and squared third moment.

References

Gerlovina, I. and Hubbard, A.E. (2019). Computer algebra and algorithms for unbiased moment estimation of arbitrary order. Cogent Mathematics & Statistics, 6(1).

See Also

uM for one-sample unbiased estimates.

Examples

nsmp <- 23
smp <- rgamma(nsmp, shape = 3)
treatment <- sample(0:1, size = nsmp, replace = TRUE)
uMpool(smp, treatment, 6)

[Package Umoments version 0.1.1 Index]