Does Excel 2010+ use the Mersenne Twister (MT19937) algorithm for Pseudo Random Number Generation (PRNG) using the RAND() function?
This has been a nagging question for some time now, with "hints" that it indeed does. A relatively thorough search turns up no definitive documentation. The most direct indication is perhaps given by Guy Melard [Ref 9] where he tests Excel 2010's RAND()
function using the Crush battery of tests in TestU01 by L'Ecuyer & Simard. Melard references a "semi-official" indication that Microsoft did indeed implement MT19937 for the RAND() function in Excel 2010, but this reference no longer seems to be
available. http://office.microsoft.com/enus/excel-help/about-solver-HP005198368.aspx?pid=CH010004571033.
The other references below document the history of the statistical suitability of the RNG and probability distributions in various versions of Excel. This includes the Wichmann-Hill PRNG implementations supposedly (arguably) used in Excel 2003 & 2007 for
random number generation. But still, we have no answer as to which PRNG algorithm is used in Excel 2010. Any help would be much appreciated. Thanks.
[Ref 1] B. McCullough, B. Wilson. On the Accuracy of Statistical Procedures in Microsoft Excel 97.
Computational Statistics & Data Analysis. Vol. 31 No. 1, pp 27-37. July 1999.
http://users.df.uba.ar/cobelli/LaboratoriosBasicos/excel97.pdf
[Ref 2]L. Knüsel. On the accuracy of the statistical distributions in Microsoft Excel 97. Computational Statistics & Data Analysis. Vol. 26 No. 3, pp 375-377. January 1998.
http://www.sciencedirect.com/science/article/pii/S0167947397817562
[Ref 3]B. McCullough, B. Wilson. On the Accuracy of Statistical Procedures in Microsoft Excel 2000 and Excel XP.
Computational Statistics & Data Analysis. Vol.40 No. 4, pp 713-721. October 2002.
https://www.researchgate.net/publication/222672996_On_the_accuracy_of_statistical_procedures_in_Microsoft_Excel_2000_and_Excel_XP/links/00b4951c314aac4702000000.pdf
[Ref 4] B. McCullough, B. Wilson. On the Accuracy of Statistical Procedures in Microsoft Excel 2003.
Computational Statistics & Data Analysis. Vol.49. No. 4, pp 1244-1252. June 2005.
http://www.pucrs.br/famat/viali/tic\_literatura/artigos/planilhas/msexcel.pdf
[Ref 5] L. Knüsel. On the accuracy of statistical distributions in Microsoft Excel 2003. Computational Statistics & Data Analysis, Vol. 48, No. 3, pp 445-449. March 2005.
http://www.sciencedirect.com/science/article/pii/S0167947304000337
[Ref 6] B. McCullough, D.Heiser. On the Accuracy of Statistical Procedures in Microsoft Excel 2007.
Computational Statistics & Data Analysis. Vol.52. No. 10, pp 4570-4578. June 2008.
http://users.df.uba.ar/mricci/F1ByG2013/excel2007.pdf
[Ref 7] A. Yalta. The Accuracy of Statistical Distributions in Microsoft^®^ Excel 2007. Computational Statistics & Data Anlaysis. Vol. 52 No. 10, pp 4579 – 4586. June 2008.
http://www.sciencedirect.com/science/article/pii/S0167947308001618
[Ref 8] B. McCullough. Microsoft Excel’s ‘Not The Wichmann-Hill’ Random Number Generators. Computational Statistics and Data Analysis. Vol.52. No. 10, pp 4587-4593. June 2008.
http://www.sciencedirect.com/science/article/pii/S016794730800162X
[Ref 9] G. Melard. On the Accuracy of Statistical Procedures in Microsoft Excel 2010. Computational Statistics. Vol.29 No. 5, pp 1095-1128. October 2014.
http://homepages.ulb.ac.be/~gmelard/rech/gmelard_csda23.pdf
[Ref 10] L. Knüsel. On the Accuracy of Statistical Distributions in Microsoft Excel 2010. Department of Statistics - University of Munich, Germany.
http://www.csdassn.org/software_reports/excel2011.pdf