1. Comparison of Pseudorandom Number Generators and Their Application for Uncertainty Estimation Using Monte Carlo Simulation
- Author
-
Karan Malik, Jiji Pulikkotil, and Anjali Sharma
- Subjects
Pseudorandom number generator ,Physics and Astronomy (miscellaneous) ,Random number generation ,Computer science ,Monte Carlo method ,Degrees of freedom (statistics) ,Estimator ,Probability distribution ,Measurement uncertainty ,Algorithm ,Randomness - Abstract
Generating random numbers is prerequisite to any Monte Carlo method implemented in a computer program. Therefore, identifying a good random number generator is important to guarantee the quality of the output of the Monte Carlo method. However, sequences of numbers generated by means of algorithms are not truly random, but having certain control on its randomness essentially makes them pseudo-random. What then matters the most is that the simulation of a physical variable with a probability distribution, needs to have the same distribution generated by the algorithm itself. In this perspective, considering the example of gauge block calibration given in "Evaluation of measurement data—Supplement 1 to the “Guide to the expression of uncertainty in measurement”—Propagation of distributions using a Monte Carlo method", we explore the properties and output of three commonly used random number generators, namely the linear congruential (LC) generator, Wichmann-Hill (WH) generator and the Mersenne-Twister (MT) generator. Extensive testing shows that the performance of the MT algorithm transcends that of LC and WH generators, particularly in its time of execution. Further, these generators were used to estimate the uncertainty in the measurement of the length, with input variables having different probability distributions. While, in the conventional GUM approach the output distribution appears to be Gaussian-like, we from our Monte-Carlo calculations find it to be a students' t-distribution. Applying the Welch-Satterthwaite equation to the result of the Monte Carlo simulation, we find the effective degrees of freedom to be 16. On the other hand, using a trial–error fitting method to determine the nature of the output PDF, we find that the resulting distribution is a t-distribution with 46 degrees of freedom. Extending these results to calculate the expanded uncertainty, we find that the Monte-Carlo results are consistent with the recently proposed mean/median-based unbiased estimators which takes into account the artifact of transformation distortion.
- Published
- 2021
- Full Text
- View/download PDF