# uM2M3pool: Pooled central moment estimates - two-sample In innager/Umoments: Unbiased Central Moment Estimates

## Description

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

## Usage

 `1` ```uM2M3pool(m2, m3, m5, n_x, n_y) ```

## Arguments

 `m2` naive biased variance estimate m[2] = mean(c((X - X-bar)^2, (Y - Y-bar)^2)) for vectors `X` and `Y`. `m3` naive biased third central moment estimate m[3] = mean(c((X - X-bar)^3, (Y - Y-bar)^3)) for vectors `X` and `Y`. `m5` naive biased fifth central moment estimate m[5] = mean(c((X - X-bar)^5, (Y - Y-bar)^5)) for vectors `X` and `Y`. `n_x` number of observations in the first group. `n_y` number of observations in the second group.

## Value

Pooled estimate of a product of second and third central moments μ[2] μ[3], where μ[2] and μ[3] are second and third central moments respectively.

Other pooled estimates (two-sample): `uM2M4pool`, `uM2pool`, `uM2pow2pool`, `uM2pow3pool`, `uM3pool`, `uM3pow2pool`, `uM4pool`, `uM5pool`, `uM6pool`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```nx <- 10 ny <- 8 shp <- 3 smpx <- rgamma(nx, shape = shp) - shp smpy <- rgamma(ny, shape = shp) mx <- mean(smpx) my <- mean(smpy) m <- numeric(5) for (j in 2:5) { m[j] <- mean(c((smpx - mx)^j, (smpy - my)^j)) } uM2M3pool(m[2], m[3], m[5], nx, ny) ```