uM2pow3pool: Pooled central moment estimates - two-sample

In Umoments: Unbiased Central Moment Estimates

Pooled central moment estimates - two-sample

Description

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

Usage

uM2pow3pool(m2, m3, m4, m6, n_x, n_y)

Arguments

m2	naive biased variance estimate m_2 = 1/(n_x + n_y) \sum_{i = 1}^{n_x} ((X_i - \bar{X})^2 + \sum_{i = 1}^{n_y} ((Y_i - \bar{Y})^2 for vectors X and Y.
m3	naive biased third central moment estimate m_3 = 1/(n_x + n_y) \sum_{i = 1}^{n_x} ((X_i - \bar{X})^3 + \sum_{i = 1}^{n_y} ((Y_i - \bar{Y})^3 for vectors X and Y.
m4	naive biased fourth central moment estimate m_4 = 1/(n_x + n_y) \sum_{i = 1}^{n_x} ((X_i - \bar{X})^4 + \sum_{i = 1}^{n_y} ((Y_i - \bar{Y})^4 for vectors X and Y.
m6	naive biased sixth central moment estimate m_6 = 1/(n_x + n_y) \sum_{i = 1}^{n_x} ((X_i - \bar{X})^6 + \sum_{i = 1}^{n_y} ((Y_i - \bar{Y})^6 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 cubed variance central moment \mu_2^3, where \mu_2 is a variance.

See Also

Other pooled estimates (two-sample): uM2M3pool(), uM2M4pool(), uM2pool(), uM2pow2pool(), uM3pool(), uM3pow2pool(), uM4pool(), uM5pool(), uM6pool()

Examples

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(6)
for (j in 2:6) {
  m[j] <- mean(c((smpx - mx)^j, (smpy - my)^j))
}
uM2pow3pool(m[2], m[3], m[4], m[6], nx, ny)

Umoments documentation built on Oct. 2, 2024, 9:08 a.m.