maxwellQlink | R Documentation |

Computes the `maxwellQlink`

transformation, its inverse and the
first two derivatives.

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

`theta` |
Numeric or character. See below for further details. |

`p` |
Numeric. A single value between 0 and 1.
It is the |

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

In the VGLM/VGAM quantile regression context, this link function
can be used to model any `p`

–quantile of the
Maxwell distribition. It is the `maxwellQlink`

transformation
given by

`\sqrt{ 2~\textrm{\texttt{qgamma(p, 1.5) / a.}}}`

Here, `a`

is positive parameter as in
`maxwell`

whereas `qgamma`

is the quantile
function of the gamma distribution.

Numerical values of `a`

or `p`

out of range will
result in `Inf`

, `-Inf`

, `NA`

or `NaN`

correspondingly.

In particular, arguments `inverse`

and `deriv`

are
disregarded if `theta`

is character.
Also, if `inverse = TRUE`

and `deriv = 0`

, then argument
`theta`

becomes `\eta`

. See `Links`

for further details about this.

For `deriv = 0`

, the `maxwellQlink`

transformation of
`theta`

, when `inverse = FALSE`

. If `inverse = TRUE`

,
then the inverse given by `2*qgamma(p, 1.5) / theta^2 `

is returned.

For `deriv = 1`

, this function returns the derivative
`d`

`eta`

/ `d`

`theta`

,
if `inverse = FALSE`

. Else, the reciprocal
`d`

`theta`

/ `d`

`eta`

as a function of `theta`

.

If `deriv = 2`

, then the second order derivatives in terms of
`theta`

are accordingly returned.

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.

`maxwell`

,
`Links`

.

```
## E1. maxwellQlink() and its inverse ##
p <- 0.25 ## Modeling the first quartile
my.a <- seq(0, 5, by = 0.1)[-1]
max(my.a - maxwellQlink(maxwellQlink(my.a, p = p), p = p, inverse =TRUE)) ## Zero
## E2. The first two values are negative, NaN is returned ##
maxwellQlink(theta = c(-0.15, -0.10, 0.25, 0.35) , p = p, inverse = FALSE)
maxwellQlink(theta = c(-0.15, -0.10, 0.25, 0.35) , p = p, inverse = TRUE)
## E3. Plot of the maxwellQlink() and its inverse ##
## Note, inverse = TRUE implies that argument 'theta' becomes 'eta'. ##
#--- THE LINK
plot(maxwellQlink(theta = my.a, p = p) ~ my.a,
type = "l", col = "blue", lty = "dotted", lwd = 3,
xlim = c(-0.1, 10), ylim = c(-0.1, 5), las = 1,
main = c("Blue is maxwellQlink(), green is the inverse"),
ylab = "eta = maxwellQlink", xlab = "theta")
abline(h = 0, v = 0, lwd = 2)
#--- THE INVERSE
lines(my.a, maxwellQlink(theta = my.a, p = p,inv = TRUE),
col = "green", lwd = 2, lty = "dashed")
lines(my.a, my.a) # Tracing the identity function for double--check
```

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