View source: R/contsDistQlinks.R

rayleighQlink | R Documentation |

Computes the `rayleighQlink`

transformation, its inverse and the
first two derivatives.

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

`theta` |
Numeric or character. It is |

`p` |
Numeric. A single value between 0.0 and 1.0.
It is the |

`bvalue, inverse, deriv, short, tag` |
See |

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.

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`

.

Numerical instability may occur for values `theta`

too close
to zero. Use argument `bvalue`

to replace them before
computing the link.

V. Miranda and Thomas W. Yee.

`rayleigh`

,
`Links`

.

```
## 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.

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