## Description

Calculate link function and up to one derivative for families known to the package.

## Usage

 `1` ```link(xi, fam, deriv = 0, delta) ```

## Arguments

 `xi` mean value parameter value, a numeric vector. `fam` an object of class `"astfam"` produced by one of the family functions (see `families`) specifying the exponential family. `deriv` the number of derivatives wanted. Must be either zero or one. `delta` direction in which limit is taken. Link function is for family that is limit of family specified, limit being for distributions with canonical parameter theta + s delta, the limit being as s to infinity. May be missing, in which case delta = 0 is assumed, which is the same as no limit being taken.

## Value

a list containing some of the following components:

 `zeroth` the value of the link function at xi, a vector of dimension d, where d

is the dimension of xi.

 `first` the value of the first derivative at xi, a d by d matrix, where d is the dimension of xi or a scalar if xi is scalar.

## Note

Not intended for use by ordinary users. Provides R interface for testing to C code called by many other functions in the package.

`families` and `cumulant`
 ```1 2``` ```link(0.3, fam.bernoulli(), deriv = 1) link(0.3, fam.bernoulli(), deriv = 1, delta = 1) ```
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