Variance of the Modified Half-Normal Distribution

Computes $\mathrm{Var}(X)$ for $X \sim \mathrm{MHN}(\alpha, \beta, \gamma)$.

Usage

mhn_var(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 formula (Sun et al., 2023, Lemma 2c): $$\mathrm{Var}(X) = \frac{\alpha}{2\beta} + E(X)\left(\frac{\gamma}{2\beta} - E(X)\right)$$

For $\alpha \geq 1$, the variance satisfies $\mathrm{Var}(X) \leq 1/(2\beta)$ (Sun et al., 2023, Lemma 4c).

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 2c)

Examples

mhn_var(alpha = 2, beta = 1, gamma = 0)
#> [1] 0.2146018