TukeyGH77 (version 0.1.4)

TukeyGH: Tukey \(g\)-&-\(h\) Distribution

Description

Density, distribution function, quantile function 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, ...)

Value

Function dGH() returns the density and accommodates vector arguments A, B, g and h. The quantiles x can be either vector or matrix. This function takes about 1/5 time of gk::dgh.

Function pGH() returns the distribution function, only taking scalar arguments and vector quantiles \(q\). This function takes about 1/10 time of function gk::pgh.

Function qGH() returns the quantile function, only taking scalar arguments and vector probabilities \(p\).

Function rGH() generates random deviates, only taking scalar arguments.

Arguments

x, q

double vector, quantiles

A

double scalar, location parameter \(A=0\) by default

B

double scalar, scale parameter \(B>0\). Default \(B=1\)

g

double scalar, skewness parameter \(g=0\) by default (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 \(\log(p)\).

...

other parameters of function vuniroot2()

n

integer scalar, number of observations

p

double vector, probabilities

lower.tail

logical scalar, if TRUE (default), probabilities are \(Pr(X\le x)\) otherwise, \(Pr(X>x)\).

Examples

(x = c(NA_real_, rGH(n = 5L, g = .3, h = .1)))
dGH(x, g = c(0,.1,.2), h = c(.1,.1,.1))

p0 = seq.int(0, 1, by = .2)
(q0 = qGH(p0, g = .2, h = .1))
range(pGH(q0, g = .2, h = .1) - p0)

q = (-2):3; q[2L] = NA_real_; q
(p1 = pGH(q, g = .3, h = .1))
range(qGH(p1, g = .3, h = .1) - q, na.rm = TRUE)
(p2 = pGH(q, g = .2, h = 0))
range(qGH(p2, g = .2, h = 0) - q, na.rm = TRUE)

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