Computes \(E(X)\) for \(X \sim \mathrm{MHN}(\alpha, \beta, \gamma)\).
Usage
mhn_mean(alpha, beta, gamma)
Arguments
- alpha
Shape parameter (\(\alpha > 0\)).
- beta
Scale parameter (\(\beta > 0\)).
- gamma
Location parameter (\(\gamma \in R\)).
Details
The mean is computed as a ratio of Fox-Wright Psi functions:
$$E(X) = \frac{\Psi[(\alpha+1)/2,\, \gamma/\sqrt{\beta}]}{
\sqrt{\beta}\, \Psi[\alpha/2,\, \gamma/\sqrt{\beta}]}$$
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 2a)
Examples
mhn_mean(alpha = 2, beta = 1, gamma = 0)
#> [1] 0.8862269