qfunc/qfuncinv implementation in communications package

[Richardson, Anthony]

The function qfunc() in the communications package is currently implemented as:

 

y = 1-normcdf(x);

 

This returns 0 for values of x greater than approx. 8 (where normcdf() is close to 1).  I believe a better implementation is:

 

y = erfc(x/sqrt(2))/2;

 

A simple test to compare the two implementations is:

 

x = [0:3:18]; [qfunc(x); erfc(x/sqrt(2))/2]

 

Can the implementation of qfunc() be changed please?

 

The function qfuncinv() suffers from similar problems (it returns Inf for small arguments).  I had hoped just rewriting it in terms of erfcinv() would fix this problem too, but I found that erfcinv() is implemented in the specfun package as:

 

y= erfinv(1 – x)

 

which exhibits problems for small values of x (due to the subtraction from 1).  A better implementation of erfcinv is needed, but I don’t know what that would be.

 

Tony Richardson