Umoments (version 1.0.1)

uM2pow3: Unbiased central moment estimates

Description

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

Usage

uM2pow3(m2, m3, m4, m6, n)

Value

Unbiased estimate of cubed second central moment

\(\mu_2^3\), where \(\mu_2\) is a variance.

Arguments

m2

naive biased variance estimate \(m_2 = 1/n \sum_{i = 1}^n ((X_i - \bar{X})^2\) for a vector X.

m3

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

m4

naive biased fourth central moment estimate \(m_4 = 1/n \sum_{i = 1}^n ((X_i - \bar{X})^4\) for a vector X.

m6

naive biased sixth central moment estimate \(m_6 = 1/n \sum_{i = 1}^n ((X_i - \bar{X})^6\) for a vector X.

n

sample size.

See Also

Other unbiased estimates (one-sample): uM2(), uM2M3(), uM2M4(), uM2pow2(), uM3(), uM3pow2(), uM4(), uM5(), uM6()

Examples

n <- 10
smp <- rgamma(n, shape = 3)
m <- mean(smp)
for (j in 2:6) {
  m <- c(m, mean((smp - m[1])^j))
}
uM2pow3(m[2], m[3], m[4], m[6], n)