explink {VGAM} | R Documentation

## Exponential Link Function

### Description

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

### Usage

    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

### See Also

`Links`, `loglink`, `rcim`, `Qvar`, `uninormal`.

### Examples

    theta <- rnorm(30)
    explink(theta)
    max(abs(explink(explink(theta), inverse = TRUE) - theta))  # Should be 0

[Package VGAM version 1.1-1 Index]