# rayleighQlink: Link functions for the quantiles of several 1-parameter... In VGAMextra: Additions and Extensions of the 'VGAM' Package

## Link functions for the quantiles of several 1–parameter continuous distributions

### Description

Computes the rayleighQlink transformation, its inverse and the first two derivatives.

### Usage

  rayleighQlink(theta, p = stop("Argument 'p' must be specified."),
bvalue = NULL, inverse = FALSE,
deriv = 0, short = TRUE, tag = FALSE)



### Arguments

 theta Numeric or character. It is \theta by default, although it may be \eta. See Links for additional details about this. p Numeric. A single value between 0.0 and 1.0. It is the p–quantile to be modeled by this link function. bvalue, inverse, deriv, short, tag See Links.

### Details

This link function directly models any p–quantile of the Rayleigh distribution specified by the argument p. It is called the rayleighQlink transformation defined as

b \sqrt{-2 \log(1 - p)},

where b > 0 is a scale parameter as in rayleigh.

Numerical values of b or p out of range may result in Inf, -Inf, NA or NaN.

If theta is character, then arguments inverse and deriv are discarded.

### Value

For deriv = 0, the rayleighQlink transformation of theta, when inverse = FALSE. If inverse = TRUE, then this function returns theta / sqrt(-2 log(1 - p)).

For deriv = 1, then the function returns d eta / d theta, if inverse = FALSE. If inverse = TRUE, then d theta / d eta as a function of theta.

If deriv = 2, then the second order derivatives in terms of theta.

### Note

Numerical instability may occur for values theta too close to zero. Use argument bvalue to replace them before computing the link.

### Author(s)

V. Miranda and Thomas W. Yee.

rayleigh, Links.

### Examples

 ## E1. rayleighQlink() and its inverse ##
p <- 0.50                           ## Modeling the median
my.b <- seq(0, 5, by = 0.1)[-1]
max(my.b - rayleighQlink(rayleighQlink(my.b, p = p), p = p, inverse  =TRUE)) ## Zero

## E2. Special values ##
rayleighQlink(theta = c(Inf, -Inf, NA, NaN), p = p)

## E3. Use of argument 'bvalue' ##
rayleighQlink(theta = seq(-0.2, 1.0, by = 0.1), p = p)  # WARNING: NaNs if theta <= 0
rayleighQlink(theta = seq(-0.2, 1.0, by = 0.1), p = p, bvalue = .Machine\$double.xmin)



VGAMextra documentation built on Nov. 2, 2023, 5:59 p.m.