Package {TukeyGH77}

Type:	Package
Title:	Tukey g-&-h Distribution
Version:	0.2.0
Date:	2026-07-16
Description:	Density, cumulative density, quantile and simulation of the 4-parameter Tukey g-and-h (1977) distributions. The quantile-based transformation (Hoaglin 1985 <doi:10.1002/9781118150702.ch11>) and its reverse transformation.
License:	GPL-2
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.6.0)
Imports:	rstpm2
Config/roxygen2/version:	8.0.0
Config/roxygen2/markdown:	TRUE
NeedsCompilation:	no
Packaged:	2026-07-16 15:16:12 UTC; tingtingzhan
Author:	Tingting Zhan [aut, cre]
Maintainer:	Tingting Zhan <tingtingzhan@gmail.com>
Repository:	CRAN
Date/Publication:	2026-07-16 20:50:02 UTC

TukeyGH77: Tukey g-&-h Distribution

Description

Density, cumulative density, quantile and simulation of the 4-parameter Tukey g-and-h (1977) distributions. The quantile-based transformation (Hoaglin 1985 doi:10.1002/9781118150702.ch11) and its reverse transformation.

Author(s)

Maintainer: Tingting Zhan tingtingzhan@gmail.com (ORCID)

Authors:

• Tingting Zhan tingtingzhan@gmail.com (ORCID)

References

Tukey, J.W. (1977): Modern Techniques in Data Analysis. In: NSF-sponsored Regional Research Conference at Southeastern Massachusetts University, North Dartmouth, MA.

Hoaglin, D.C. (1985): Summarizing shape numerically: The g-and-h distributions. Exploring data tables, trends, and shapes, pp. 461–513. John Wiley & Sons, Ltd, New York.

Tukey g-&-h Distribution

Description

Density, distribution, quantile and simulation for Tukey g-&-h distribution with location parameter A, scale parameter B, skewness g and elongation h.

Usage

dGH(x, A = 0, B = 1, g = 0, h = 0, log = FALSE, ...)

rGH(n, A = 0, B = 1, g = 0, h = 0)

qGH(p, A = 0, B = 1, g = 0, h = 0, lower.tail = TRUE, log.p = FALSE)

pGH(q, A = 0, B = 1, g = 0, h = 0, lower.tail = TRUE, log.p = FALSE, ...)

Arguments

Value

Density function dGH() returns double vector.

Distribution function pGH() returns double vector.

Quantile function qGH() returns double vector.

Random generator function rGH() returns double vector.

Examples

curve(pGH(x, g = .3, h = .1), from = -2.5, to = 3.5)

Derivative of z2gh() against z, on the log-scale

Description

Derivative of z2gh() against z, on the log-scale

Usage

d_z2GH(z, g, h)

Arguments

Tukey g-&-h Transformation

Description

The function z2gh() (not compute intensive) transforms standard normal quantiles z_q to Tukey g-&-h quantiles.

The function gh2z() (compute intensive!!) transforms Tukey g-&-h quantiles to standard normal quantiles z_q.

Usage

z2gh(z, g = 0, h = 0)

gh2z(q, g = 0, h = 0, ...)

Arguments

Details

Domain of standard normal quantile z to search for the function gh2z() is hard coded as (-8.3, 8.3), because stopifnot(identical(pnorm(8.3), 1)).

Value

The functions z2gh() and gh2z() both return double scalar, vector or matrix.