**A Generalised Emerson Recurrence
Relation**

On
this page you can find R functions for the calculation of univariate and
bivariate orthonormal polynomials. At this moment we provide two source files,
one for the univariate and one for the bivariate polynomials. It is our intention
to combine both into one R package.

**Univarariate
orthonormal polynomials**

The
implementation is based on Rayner et al. (2008, ANZJS, 50(3), 235-240).

- Here you can find the zipped R package. Once the
package is installed, use help(orth.poly) for help.
- The R code used to generate the example in the
paper can be downloaded here.

Some guidelines for the intallation of
the package (for Windows users only):

1.
since the package depends on the minpack.lm package, this
package should be installed first:

To
install the minpack.lm
package (it may happen that step 2 is skipped): (1) go to the Packages menu in
R; (2) select "Load package ..."; (2) select a file server; (3)
select "minpack.lm".

2.
install the orth.poly package:

You can
install the package by (1) saving the zip file to a local directory; (2) go to
the Packages menu in R; (3) select "Install package(s) from local zip
file"; (4) select the zip file; (5) go again to the Packages menu and
select "load package" and select "orth.poly" from the list.
The package is now installed.

**Bivarariate
orthonormal polynomials**

The
implementation is based on Rayner et al. (ANZJS).

·
Here you can
find the source code of the R functions.

·
The R code used to generate some of the examples presented
in the paper can be donwloaded here. The
final example is on a smooth test for the dependence structure implied by a
copula. Here you can find
some more background information that was not discussed in detail in the paper.