uM3 {Umoments}

Unbiased central moment estimates

Description

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

Usage

uM3(m3, n)

Arguments

m3

naive biased third central moment estimate m_3 = 1/n \sum_{i = 1}^n ((X_i - \bar{X})^3 for a vector X.

n

sample size.

Value

Unbiased estimate of a third central moment.

See Also

Other unbiased estimates (one-sample): uM2M3, uM2M4, uM2pow2, uM2pow3, uM2, uM3pow2, uM4, uM5, uM6

Examples

n <- 10
smp <- rgamma(n, shape = 3)
m <- mean(smp)
for (j in 2:3) {
  m <- c(m, mean((smp - m[1])^j))
}
uM3(m[3], n)