uM2M3: 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

uM2M3(m2, m3, m5, 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.
m5	naive biased fifth central moment estimate m_5 = \sum_{i = 1}^n ((X_i - \bar{X})^5 for a vector X.
n	sample size.

Value

Unbiased estimate of a product of second and third central moments \mu_2 \mu_3, where \mu_2 and \mu_3 are second and third central moments respectively.

See Also

Other unbiased estimates (one-sample): uM2(), uM2M4(), uM2pow2(), uM2pow3(), uM3(), uM3pow2(), uM4(), uM5(), uM6()

Examples

n <- 10
smp <- rgamma(n, shape = 3)
m <- mean(smp)
for (j in 2:5) {
  m <- c(m, mean((smp - m[1])^j))
}
uM2M3(m[2], m[3], m[5], n)

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