Random Number Generation

The ability to generate satisfactory sequences of uniform random numbers is one of the key links between computer science and statistics. George Marsaglia delivers a CD-Rom.

The Marsaglia random number cd-rom which contains (1) 4.8 billion random bits in sixty 10-megabyte files, (2) the diehard battery of tests of randomness,(3) files for programs that will create test files from most of the common random number generators.

Another good source is the

PLAB WWW-server established by Peter Hellekalek, Karl Entacher, Hannes Leeb, Stefan Wegenkittl and others were efficient implementations of inversive congruential generators and numerous links to other sites may be found.

A high quality multiplicative congruential generator is our proposal drand.c programmed for platforms running under MS-Dos.

Josef Leydold and co-workers offer the ANSI-C library UNU.RAN which contains universal generators from large classes of continuous and discrete distributions.

Our package WinRand is a system of C-routines and functions intended for use on microcomputers running under Windows NT. It contains up-to-date generators for more than thirty univariate continuous and discrete distributions. It may be obtained by ftp. Just download the files install.txt (for installation) and w_rand.zip (the compressed file, 1.1 Mb).

Look for the short description WIN-RAND: The System C-Rand under MS-Windows.

Recent papers, diploma theses and dissertations on this topics are:

• Meister V., Testing of random number generators. Diploma thesis in co-operation with ATRONIC, an international company producing electronic games for casinos, pp. 126, 2002.
• Stadlober E., H. Zechner (1999), The patchwork rejection method for sampling from unimodal distributions,  ACM Transactions on Modeling and Computer Simulation, Vol. 9, No. 1, 59-80.
• Zechner H., Efficient Sampling from Continuous and Discrete Distributions, Doctoral dissertation, pp. 156, 1997.
• Stadlober E., U. Dieter, Bibliography on Nonuniform Random Number Generation. Institute of Statistics, TU Graz, pp. 100, 1996.
• Piok M., Zufallszahlen aus klassischen diskreten Verteilungen mit Hilfe der Quotientenmethode. Diploma thesis, pp. 139, 1996.
• Stadlober E., F. Niederl, Generation of Non-Uniform Random Variates with C-RAND. Research Report 15, 2nd Update September 1995 with WIN-RAND1.0 by Manfred Piok, Institute of Statistics, pp. 136, 1995.
• Stadlober E., F. Niederl (1994), C--Rand: A package for generating nonuniform random variates in "Compstat 1994, Software Descriptions, pp. 63-64".
• Stadlober E., H. Zechner (1994), An efficient approach for sampling from discrete distributions in "Compstat 1994, Short Communications, pp. 132-133".
• Busswald P., Effiziente Erzeugung von Zufallszahlen aus der Zetaverteilung und Verallgemeinerten Poissonverteilung. Diploma thesis, pp. 152, 1993.
• Niederl F., Computergerechte Erzeugung und Visualisierung von Zufallszahlen mit C-Rand. Diploma thesis, 152 pp, 1993.
• Zechner H., E. Stadlober (1993),Generating beta variates via patchwork rejection, Computing 50, 1-18.
• Stadlober E., R. Kremer (1992), Sampling from discrete and continuous distributions with C-RAND, in " G.Pflug, U. Dieter (Eds.): Lecture Notes in Econ. Math. Systems 374: Simulation and Optimization, pp. 154-162".