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)

Arguments

theta

Numeric or character. It is $\theta$ by default, although it may be $\eta$. See Links for additional details about this.

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.

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.

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.

Examples

Run this code

# NOT RUN {
 ## 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)
    
# }