ISO 28640:2010

Overview

ISO 28640:2010, "Random variate generation methods", specifies algorithms and practical guidance for generating uniform and non-uniform random variates for Monte Carlo simulation and other statistical applications. The standard focuses on pseudo-random number generation (PRNG) methods and their use in simulation, experimental design and statistical quality control. Cryptographic random number generation methods are explicitly excluded.

Key topics

• Uniform pseudo-random generators: definitions, seeding, and binary operations. Coverage includes M-sequence concepts (maximum-length linear feedback shift registers) and period properties (period = 2^p − 1).
• Recommended algorithms: pentanomial GFSR (generalized feedback shift register), combined Tausworthe, Mersenne Twister. Annex B supplies program code (C and BASIC) and implementation examples; a linear congruential generator is included for information but is not recommended for complex simulations.
• Non-uniform variate generation: methods and transformation techniques for common distributions:
  • Uniform, standard beta, triangular
  • Exponential (with location and scale)
  • Normal and multivariate normal
  • Gamma, Weibull, lognormal, logistic
  • Discrete distributions: binomial, Poisson, discrete uniform
• Practical elements: symbols and binary operations (bitwise XOR, shifts), seed management, word-length considerations, and parameter tables (e.g., characteristic polynomials and parameter sets for maximal periods).
• Physical random numbers: Annex A describes tables and methods of physical random number generation (informative).

Applications

ISO 28640:2010 is applicable to:

• Researchers and industrial engineers using Monte Carlo simulation for risk analysis, reliability studies, and process modeling.
• Statisticians working on statistical quality control (SQC), design of experiments, or sampling who require reliable randomization.
• Applied mathematicians developing stochastic optimization and simulation-based algorithms.
• Software engineers implementing PRNGs and random variate libraries in simulation and analysis software.

Practical benefits include reproducible simulation results, guidance on algorithm selection for long periods and good statistical properties, and ready-to-use reference implementations.

Related standards

Normative references incorporated by ISO 28640:

• ISO/IEC 2382-1 - Information technology - Vocabulary - Fundamental terms
• ISO 3534-1 - Statistics - Vocabulary and symbols - General statistical terms
• ISO 3534-2 - Statistics - Vocabulary and symbols - Applied statistics

Keywords: ISO 28640:2010, random variate generation, pseudo-random number generator, Monte Carlo simulation, Mersenne Twister, Tausworthe, GFSR, uniform distribution, non-uniform distributions.