dist_gh: The generalised g-and-h Distribution
| dist_gh | R Documentation |
The generalised g-and-h Distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
The generalised g-and-h distribution is a flexible distribution used to model univariate data, similar to the g-k distribution. It is known for its ability to handle skewness and heavy-tailed behavior.
Usage
dist_gh(A, B, g, h, c = 0.8)
Arguments
A |
Vector of A (location) parameters. |
B |
Vector of B (scale) parameters. Must be positive. |
g |
Vector of g parameters. |
h |
Vector of h parameters. Must be non-negative. |
c |
Vector of c parameters (used for generalised g-and-h). Often fixed at 0.8 which is the default. |
Details
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
In the following, let X be a g-and-h random variable with parameters
A, B, g, h, and c.
Support: (-\infty, \infty)
Mean: Not available in closed form.
Variance: Not available in closed form.
Probability density function (p.d.f):
The g-and-h distribution does not have a closed-form expression for its density. Instead, it is defined through its quantile function:
Q(u) = A + B \left( 1 + c \frac{1 - \exp(-gz(u))}{1 + \exp(-gz(u))} \right) \exp(h z(u)^2/2) z(u)
where z(u) = \Phi^{-1}(u)
Cumulative distribution function (c.d.f):
The cumulative distribution function is typically evaluated numerically due to the lack of a closed-form expression.
See Also
gk::dgh, dist_gk
Examples
dist <- dist_gh(A = 0, B = 1, g = 0, h = 0.5)
dist
mean(dist)
variance(dist)
support(dist)
generate(dist, 10)
density(dist, 2)
density(dist, 2, log = TRUE)
cdf(dist, 4)
quantile(dist, 0.7)
