expQlink | R Documentation |

Computes the `expQlink`

transformation, its inverse and
the first two derivatives.

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

`theta` |
Numeric or character. This is |

`p` |
Numeric. A prespecified number between 0 and 1.
The particular |

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

This is a link function to model any fixed quantile, say
`\xi_p`

, of the exponential distribution.
It is called the `expQlink`

transformation and is defined as

` \log (1 - p)^{-1/\lambda},`

where `\lambda`

is positive as in
`exponential`

.

Numerical values of `\lambda`

or `p`

out of range may
result in `Inf`

, `-Inf`

, `NA`

or `NaN`

.

With `deriv = 0`

, the `expQlink`

transformation of
`theta`

for prespecified `p`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then the inverse `-log(1 - p)/theta`

.

For `deriv = 1`

, this link function returns
`d`

`eta`

/ `d`

`theta`

when `inverse = FALSE`

.
If `inverse = TRUE`

, then
`d`

`theta`

/ `d`

`eta`

as a function of
`theta`

.

Similarly, when `deriv = 2`

, the second derivatives in
terms of `theta`

are returned.

Numerical instability may occur for values `theta`

too close
to zero. Use argument `bvalue`

to replace them before
computing the link.

If `theta`

is character, then arguments `inverse`

and
`deriv`

are ignored. See `Links`

for further details.

V. Miranda and Thomas W. Yee.

`exponential`

,
`Links`

.

```
## E1. expQlink() and its inverse ##
p <- 0.25 # Modelling the first quartile.
my.theta <- seq(0, 5, by = 0.1)[-1]
my.diff <- my.theta - expQlink(expQlink(my.theta, p = p), p = p, inverse =TRUE)
summary(my.diff) # Zero
## E2. Special values ##
expQlink(theta = c(Inf, -Inf, NA, NaN), p = p)
## E3. Plot of expQlink() for different quantiles ##
plot(expQlink(my.theta, p = p) ~ my.theta,
type = "l", lty = "dotted", col = "blue", lwd = 2,
main = "expQink(p) transformation", xlab = "theta", ylab = "expQLink",
xlim = c(-0.5, 5), ylim = c(-0.5, 5))
abline(h = 0, v = 0, lwd = 2)
lines(my.theta, expQlink(my.theta, p = 0.50), col = "green", lty = "dotted", lwd = 2)
lines(my.theta, expQlink(my.theta, p = 0.75), col = "red", lty = "dotted", lwd = 2)
legend(2, 4, c("p = 0.25", "p = 0.50", "p = 0.75"), col = c("blue", "green", "red"),
lwd = c(2, 2, 2), lty = c("dotted", "dotted", "dotted"))
```

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