uM2pow3: 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

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

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.

Value

Unbiased estimate of cubed second central moment \mu_2^3, where \mu_2 is a variance.

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)

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