uM2pow2: Unbiased central moment estimates

In Umoments: Unbiased Central Moment Estimates

Unbiased central moment estimates

Description

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

Usage

uM2pow2(m2, m4, n)

Arguments

m2	naive biased variance estimate m_2 = 1/n \sum_{i = 1}^n ((X_i - \bar{X})^2 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.
n	sample size.

Value

Unbiased estimate of squared variance \mu_2^2, where \mu_2 is a variance.

See Also

Other unbiased estimates (one-sample): uM2(), uM2M3(), uM2M4(), uM2pow3(), uM3(), uM3pow2(), uM4(), uM5(), uM6()

Examples

n <- 10
smp <- rgamma(n, shape = 3)
m <- mean(smp)
for (j in 2:4) {
  m <- c(m, mean((smp - m[1])^j))
}
uM2pow2(m[2], m[4], n)

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