Variance of the sample variance

Var(s^2) = (mu4 - sigma^4 (n - 3)/(n - 1)) / n for n i.i.d. draws from a pmf, with mu4 the fourth central moment.

Usage

SampVarVar(values, probs, n)

Arguments

values, probs

Outcomes and probabilities (summing to 1).

n

Sample size, >= 2.

Value

list(var_s2, sigma2, mu4).

References

Morin, D. J. (2016). Probability: For the Enthusiastic Beginner. Createspace. Eq (3.94).

Examples

SampVarVar(1:6, rep(1 / 6, 6), 2)$var_s2
#> [1] 11.61806