Umoments (version 1.0.1)

uM3pow2: Unbiased central moment estimates

Description

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

Usage

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

Value

Unbiased estimate of squared third central moment

\(\mu_3^2\), where \(\mu_3\) is a third central moment.

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(), uM2pow3(), uM3(), 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))
}
uM3pow2(m[2], m[3], m[4], m[6], n)