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). 

 

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.