d_3 {CC}

range factors

Description

The sample range R is a biased estimator for the population standard deviation of R. For a normally distributed sample of size n, d_3(n)R is an unbiased estimator of the standard deviation of R.

Usage

d_3(n)

Arguments

n

the sample size

Value

a numeric value representing the multiplier to render R unbiased for the standard deviation of R

Author(s)

W.J. Braun

References

Montgomery, D.C. (2000) Introduction to Statistical Quality Control, Wiley

See Also

d_2

Examples

x <- rnorm(10, sd = 3)
R <- diff(range(x))
d_3(10)*R   # expected value of this is (V(R))^{1/2}