Description Usage Arguments Details Value Note Author(s) See Also Examples

View source: R/contsDistQlinks.R

Computes the `rayleighQlink`

transformation, its inverse and the
first two derivatives.

1 2 3 4 |

`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*â€“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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
## 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)
``` |

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