VGAMextra (version 0.0-6)

rayleighQlink: 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)
  

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.

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.

Author

V. Miranda and Thomas W. Yee.

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.

See Also

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)