Umoments (version 1.0.1)

uM2M4: Unbiased central moment estimates

Description

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

Usage

uM2M4(m2, m3, m4, m6, n)

Value

Unbiased estimate of a product of second and fourth central moments

\(\mu_2 \mu_4\), where \(\mu_2\) and

\(\mu_4\) are second and fourth central moments respectively.

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(), uM2pow2(), uM2pow3(), 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))
}
uM2M4(m[2], m[3], m[4], m[6], n)