Perils of simulation : parallel streams and the case of stata's rnormal command

Large-scale simulation-based studies rely on at least three properties of pseudorandom number sequences: they behave in many ways like truly random numbers; they can be replicated; and they can be generated in parallel. There has been some divergence, however, between empirical techniques employing random numbers, and the standard battery of tests used to validate them. A random number generator that passes tests for any single stream of random numbers may fail the same tests when it is used to generate multiple streams in parallel. The lack of systematic testing of parallel streams leaves statistical software with important potential vulnerabilities. This paper shows one such vulnerability in Stata's rnormal function that went unnoticed for almost four years, and how to detect it. It then shows practical implications for the use of parallel streams in existing software.