Excess Kurtosis of the Modified Half-Normal Distribution

Computes the excess kurtosis \(\gamma_2 = E[(X - \mu)^4] / \sigma^4 - 3\) for \(X \sim \mathrm{MHN}(\alpha, \beta, \gamma)\).

Usage

mhn_kurtosis(alpha, beta, gamma)

Arguments

alpha: Shape parameter (\(\alpha > 0\)).
beta: Scale parameter (\(\beta > 0\)).
gamma: Location parameter (\(\gamma \in R\)).

Value

A numeric scalar.

Details

Uses the moment recurrence (Sun et al., 2023, Lemma 2b) to compute raw moments up to fourth order, then converts to central moments.

References

Sun, J., Kong, M., & Pal, S. (2023). The Modified-Half-Normal distribution: Properties and an efficient sampling scheme. Communications in Statistics - Theory and Methods, 52(5), 1507–1536. (Lemma 2b)

Examples

mhn_kurtosis(alpha = 2, beta = 1, gamma = 0)
#> [1] 0.2450893