## 12 September 2012

### Part 6: T-SQL Implementation of NORMDIST / NORM.S.DIST

This is Part 6 of a set of posts. The other posts are:
Part 1: Introduction
Part 2: Probability Density Function Implementation
Part 3: Cumulative Distribution Function Implementation 1
Part 4: Cumulative Distribution Function Implementation 2
Part 5: Cumulative Distribution Function Implementation 3
Part 6: References and Notes

# References and Notes

As stated in Part 1 the implementations presented in this series of posts are my own, however I conducted no original research in their development.
In this part I list the sources I used while preparing this series of posts as well as notes and additional sources of interest.

### Main Sources

Wikipedia article on the Normal Distribution - the Wikipedia article was my first stop when looking for information for these series of posts. It contains the basic information and formulas for the PDF and CDF functions, but more important the section about numerical approximations contains a reference to algorithm 26.2.17 from Abramowitz & Stegun (1964) used in Part 4
Milton Abramowitz and Irene Stegun (1964) - Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables - referred in these posts as "Abramowitz & Stegun (1964)"; this book contains a wide array of formulas and approximation in several fields. The Wikipedia article has more information about this work.
The approximations used in Part 3 and Part 4 are taken from this source.
W. J. Cody (1969) - Rational Chebyshev Approximations for the Error Function, Mathematics of Computation, Vol. 23, No. 107 (Jul., 1969), pp. 631-637 - Referred in these posts as "W. J. Cody (1969)", I came accross this paper from one of the pioneers in numerical analysis while looking for Hart (1968) (see Addtional References below) and decided to use his approximation for the "ultimate" implementation in Part 5.

Improvents in Excel 2007 and 2010 are discussed in the following sources:

The white paper in the last reference in particular is very interesting as it contains a primer on common approximation methods.