uM3pow2: Unbiased central moment estimates In innager/Umoments: Unbiased Central Moment Estimates

Description

Calculate unbiased estimates of central moments and their powers and products.

Usage

 `1` ```uM3pow2(m2, m3, m4, m6, n) ```

Arguments

 `m2` naive biased variance estimate m[2] = mean((X - X-bar)^2) for a vector `X`. `m3` naive biased third central moment estimate m[3] = mean((X - X-bar)^3) for a vector `X`. `m4` naive biased fourth central moment estimate m[4] = mean((X - X-bar)^4) for a vector `X`. `m6` naive biased sixth central moment estimate m[6] = mean((X - X-bar)^6) for a vector `X`. `n` sample size.

Value

Unbiased estimate of squared third central moment μ[3]^2, where μ[3] is a third central moment.

Other unbiased estimates (one-sample): `uM2M3`, `uM2M4`, `uM2pow2`, `uM2pow3`, `uM2`, `uM3`, `uM4`, `uM5`, `uM6`
 ```1 2 3 4 5 6 7``` ```n <- 10 smp <- rgamma(n, shape = 3) m <- mean(smp) for (j in 2:6) { m <- c(m, mean((smp - m[1])^j)) } uM3pow2(m[2], m[3], m[4], m[6], n) ```