Calculate unbiased estimates of central moments and their powers and products up to specified order.
uM(smp, order)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.
sample.
highest order of the estimates to calclulate. Estimates of lower orders will be included.
Unbiased 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 (\(\mu_2^2\)), fifth order - of fifth moment and a product of second and third moments (\(\mu_2 \mu_3\)), sixth order - of sixth moment, a product of second and fourth moments (\(\mu_2 \mu_4\)), squared third moment (\(\mu_3^2\)), and cubed variance (\(\mu_2^3\)).
Gerlovina, I. and Hubbard, A.E. (2019). Computer algebra and algorithms for unbiased moment estimation of arbitrary order. Cogent Mathematics & Statistics, 6(1).
uMpool for two-sample pooled estimates.
smp <- rgamma(10, shape = 3)
uM(smp, 6)
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