Computing the Normal Distribution

I teach options, so I am interested in how accurately different software packages compute the cumulative normal distribution function. Not being a statistician, my usual approach is to compare different packages and look for discrepancies. A few years ago I noticed a tiny discrepancy in option prices computed using Excel and OpenOffice. I became curious, and started checking the calculation of the area under the curve of the standard normal distribution from minus infinity to -5.5. I found agreement between Matlab and Gnumeric, a free, open-source spreadsheet. Everything else differed.

I am revising my derivatives text, so I checked again. Things appear to have changed for the better. At least there is convergence among the different programs.

Recent versions of Matlab and Gnumeric return the same values as several years ago. The current version of Octave matches Gnumeric, as does R. Excel appears to have caught up with Gnumeric (wait, shouldn't that have been the other way around??), and Libreoffice 3.5 comes much closer than it did.

It's hard to generalize other than to note that both commercial and open source software had hits and misses a few years ago. Excel has long been pilloried for sloppy statistical programming, so it's good to see that Microsoft may finally be getting its act together. The percentage differences below were all computed in Excel 2010.

Blogger's table support is non-existent, so you may not be able to read the table below. Here is a pdf version.

Software	Function	Value	% diff from Gnumeric
Gnumeric 1.6.3	Normsdist(-5.5)	1.89895624658877E-08	0.0000E+00
Matlab 2006b	Normcdf(-5.5)	1.89895624658877E-08	0.0000E+00
Octave 3.0.1	Normcdf(-5.5)	1.89895624780334E-08	6.3960E-10
Excel 2007	Normsdist(-5.5)	1.89895624780334E-08	6.3960E-10
OO 2.4.1/3.0	Normsdist(-5.5)	1.89901047664698E-08	2.8558E-05
Excel 2010	Normsdist(-5.5)	1.89895624658877E-08	-5.2272E-16
R 2.15.1	pnorm(-5.5)	1.89895624658877E-08	0.0000E+00
Octave 3.6.1	Normcdf(-5.5)	1.89895624658877E-08	0.0000E+00
Libreoffice 3.5.4	Normsdist(-5.5)	1.89895624658900E-08	1.2110E-13