Package 'TukeyGH77'

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 [email protected] (ORCID)

Authors:

• Tingting Zhan [email protected] (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.

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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

x	double vector, quantiles $x$, missingness is allowed for function fitdistrplus::fitdist()
A	double scalar, location parameter $A$, default $A=0$,
B	double scalar, scale parameter $B>0$, default $B=1$
g	double scalar, skewness parameter $g$, default $g=0$ (i.e., no skewness)
h	double scalar, elongation parameter $h\geq 0$, default $h=0$ (i.e., no elongation)
log, log.p	logical scalar, if TRUE, probabilities $p$ are given as $\log(p)$.
...	additional parameters of function gh2z()
n	integer scalar, number of observations
p	double vector, probabilities $p$, missingness is not allowed
lower.tail	logical scalar, if TRUE (default), probabilities are $Pr(X\le x)$ otherwise, $Pr(X>x)$.
q	double vector, quantiles $q$, missingness is not allowed

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

dGH(x, g = .3, h = .1) |> curve(from = -2.5, to = 3.5)
pGH(x, g = .3, h = .1) |> curve(from = -2.5, to = 3.5)
qGH(x, g = .3, h = .1) |> curve(from = 0, to = 1)

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