Umoments (version 0.1.0)

uM4: Unbiased central moment estimates

Description

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

Usage

uM4(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 a fourth central moment.

See Also

Other unbiased estimates (one-sample): uM2M3, uM2M4, uM2pow2, uM2pow3, uM2, uM3pow2, uM3, uM5, uM6

Examples

# NOT RUN {
n <- 10
smp <- rgamma(n, shape = 3)
m <- mean(smp)
for (j in 2:4) {
  m <- c(m, mean((smp - m[1])^j))
}
uM4(m[2], m[4], n)
# }