expQlink {VGAMextra} | R Documentation |
Link functions for the quantiles of several 1–parameter continuous distributions.
Description
Computes the expQlink
transformation, its inverse and
the first two derivatives.
Usage
expQlink(theta, p = stop("Argument 'p' must be entered."),
bvalue = NULL, inverse = FALSE,
deriv = 0, short = TRUE, tag = FALSE)
Arguments
theta |
Numeric or character. This is |
p |
Numeric. A prespecified number between 0 and 1.
The particular |
bvalue , inverse , deriv , short , tag |
See |
Details
This is a link function to model any fixed quantile, say
, of the exponential distribution.
It is called the
expQlink
transformation and is defined as
where is positive as in
exponential
.
Numerical values of or
out of range may
result in
Inf
, -Inf
, NA
or NaN
.
Value
With deriv = 0
, the expQlink
transformation of
theta
for prespecified when
inverse = FALSE
.
If inverse = TRUE
, then the inverse -log(1 - p)/theta
.
For deriv = 1
, this link function returns
eta
/
theta
when inverse = FALSE
.
If inverse = TRUE
, then
theta
/
eta
as a function of
theta
.
Similarly, when deriv = 2
, the second derivatives in
terms of theta
are returned.
Note
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.
Author(s)
V. Miranda and Thomas W. Yee.
See Also
Examples
## 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"))