The error function erf(x) and the normal distribution Φ(x) are essentially the same function. The former is more common in math, the latter in statistics. I often have to convert between the two.
It’s a simple exercise to move between erf(x) and Φ(x), but it’s tedious and error-prone, especially when you throw in variations on these two functions such as their complements and inverses. Some time ago I got sufficiently frustrated to write up the various relationships in a LaTeX file for future reference. I was using this file yesterday and thought I should post it as a PDF file in case it could save someone else time and errors.
{ 4 comments… read them below or add one }
Blaise F Egan 10.08.08 at 02:21
Very helpful. Thanks!
jyotsna 11.21.08 at 12:04
That was very useful ! thanks for your post !
Theodore 12.09.08 at 08:04
Greetings,
Thanks for the post. Shouldn’t the last term in the third equation in your pdf file be erf(x) and not erfc(x) ?
Regards
John 12.09.08 at 08:47
Yes, you are right. Thanks for pointing out the error, no pun intended. I’ve corrected the file.