M2M3one: Unbiased central moment estimates

In innager/edgee: Edgeworth Expansions and Higher-Order Inference

Unbiased central moment estimates

Description

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

Usage

M2M3one(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: M2M3two(), M2M4one(), M2M4two(), M2one(), M2pow2one(), M2pow2two(), M2pow3one(), M2pow3two(), M2two(), M3one(), M3pow2one(), M3pow2two(), M3two(), M4one(), M4two(), M5one(), M5two(), M6one(), M6two()

Examples

n <- 10
smp <- rgamma(n, shape = 3)
for (j in 2:6) {
  assign(paste("m", j, sep = ""), mean((smp - mean(smp))^j))
}
M2M3one(m2, m3, m5, n) 

innager/edgee documentation built on April 24, 2024, 8:14 p.m.