rayleighMlink | R Documentation |

The `rayleighMlink`

and the `maxwellMlink`

transformations, their inverse and the first two derivatives.

```
rayleighMlink(theta, bvalue = NULL, inverse = FALSE,
deriv = 0, short = TRUE, tag = FALSE)
maxwellMlink(theta, bvalue = NULL, inverse = FALSE,
deriv = 0, short = TRUE, tag = FALSE)
```

`theta` |
Numeric or character. It is |

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

`rayleighMlink`

and `maxwellMlink`

are link functions
to model the mean of the Rayleigh distirbution,
(`rayleigh`

),
and the mean of the Maxwell distribution,
(`maxwell`

),
respectively.

Both links are somehow defined as the
` \log {\tt{theta}} `

plus an *offset*. Specifcally,

` {\tt{rayleighMlink}}(b) = \log ( b * \gamma(0.5) / sqrt{2} ),`

where `b > 0`

is a scale parameter as in
`rayleigh`

; and

` {\tt{maxwellhMlink}}(b) = \log ( a^{-1/2} * sqrt{8 / \pi} ).`

Here, `a`

is positive as in `maxwell`

.

Nonâ€“positive values of `a`

and/or `b`

will result in
`NaN`

, whereas values too close to zero will return
`Inf`

or `-Inf`

.

For `deriv = 0`

, the corresponding transformation of
`theta`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then `theta`

becomes `\eta`

, and
the inverse transformations

I) `exp(theta) * sqrt`

(2) / `gamma(0.5)`

for `rayleighMlink`

, and

II) `8`

` * exp(-2 * theta) `

/ `gamma(0.5)`

`^2`

for
`maxwellMlink`

,

are returned.

For `deriv = 1`

,
`d`

`eta`

/ `d`

`theta`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then
`d`

`theta`

/ `d`

`eta`

as a function of
`theta`

.

When `deriv = 2`

, the second derivatives in
terms of `theta`

are returned.

Values of `a`

or `b`

out of range, e.g. when covariates
involved, may cause numerical instability.
Use argument `bvalue`

to replace them before computing any link.

If `theta`

is character, then arguments `inverse`

and
`deriv`

are ignored. See `Links`

for further details.

V. Miranda and Thomas W. Yee.

`maxwell`

,
`rayleigh`

`Links`

.

```
## The link and its inverse ##
theta <- 0.1 + 1:10
eta <- maxwellMlink(maxwellMlink(theta = theta), inverse =TRUE)
summary(eta - theta) # Zero
eta <- rayleighMlink(rayleighMlink(theta = theta), inverse =TRUE)
summary(eta - theta) # Zero
## Modelling the mean of the Maxwell distribution ##
set.seed(17010401)
rate <- maxwellMlink(theta = 2, inverse = TRUE) # ~ 0.046
mdata <- data.frame(y = rmaxwell(1000, rate = rate ))
fit <- vglm(y ~ 1, maxwell(link = "maxwellMlink"),
data = mdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)
Coef(fit)
```

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