New implementations of qfunc, qfuncinv, erfcinv

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

y = 1 – normcdf(x)

This implementation returns 0 for values of x greater than about 8.3 (qfunc(8.3) is actually about 5.205E-17 and such small probabilities are or interest when working with bit error probabilities in binary comm problems). I’ve attached an implementation that calculates qfunc() using:

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

This returns non-zero values for x less than about 39.

There are similar problems with the current implementations of erfcinv and qfuncinv (problems here with very small arguments). To fix these I had originally implemented qfuncinv using a rational approx. from a numerical methods text. I eventually found a much better method for implementing erfcinv here: http://home.online.no/~pjacklam/notes/invnorm/index.html and rewrote qfuncinv to use that implementation. (The current implementation of qfuncinv returns Inf for arguments less than 1E-17 or so. The attached implementation returns finite values for arguments down to about 1E-300.) The erfcinv web site says that the code can be used for any purpose.

If would be nice to have a built-in (C ) implementation of erfcinv, code is available at the web site mentioned above.

Anyway, I hope someone else finds these useful.

Tony Richardson

From:	Richardson, Anthony
Subject:	New implementations of qfunc, qfuncinv, erfcinv
Date:	Wed, 6 Feb 2013 13:43:54 +0000