uM5: Unbiased central moment estimates

In Umoments: Unbiased Central Moment Estimates

Description

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

Usage

uM5(m2, m3, m5, n)

Arguments

m2	naive biased variance estimate m[2] = mean((X - X-bar)^2) for a vector X.
m3	naive biased third central moment estimate m[3] = mean((X - X-bar)^3) for a vector X.
m5	naive biased fifth central moment estimate m[5] = mean((X - X-bar)^5) for a vector X.
n	sample size.

Value

Unbiased estimate of a fifth central moment.

See Also

Other unbiased estimates (one-sample): uM2M3, uM2M4, uM2pow2, uM2pow3, uM2, uM3pow2, uM3, uM4, 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))
}
uM5(m[2], m[3], m[5], n)

Umoments documentation built on March 26, 2020, 7:18 p.m.