## Description

Computes the exponential transformation, including its inverse and the first two derivatives.

## Usage

 `1` ```explink(theta, bvalue = NULL, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE) ```

## Arguments

 `theta` Numeric or character. See below for further details.
 `bvalue` See `clogloglink`. `inverse, deriv, short, tag` Details at `Links`.

## Details

The exponential link function is potentially suitable for parameters that are positive. Numerical values of `theta` close to negative or positive infinity may result in `0`, `Inf`, `-Inf`, `NA` or `NaN`.

## Value

For `explink` with `deriv = 0`, the exponential of `theta`, i.e., `exp(theta)` when `inverse = FALSE`. And if `inverse = TRUE` then `log(theta)`; if `theta` is not positive then it will return `NaN`.

For `deriv = 1`, then the function returns d `eta` / d `theta` as a function of `theta` if `inverse = FALSE`, else if `inverse = TRUE` then it returns the reciprocal.

Here, all logarithms are natural logarithms, i.e., to base e.

## Note

This function has particular use for computing quasi-variances when used with `rcim` and `uninormal`.

Numerical instability may occur when `theta` is close to negative or positive infinity. One way of overcoming this (one day) is to use `bvalue`.

## Author(s)

Thomas W. Yee

`Links`, `loglink`, `rcim`, `Qvar`, `uninormal`.
 ```1 2 3``` ```theta <- rnorm(30) explink(theta) max(abs(explink(explink(theta), inverse = TRUE) - theta)) # Should be 0 ```