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.

生成随机数是在计算机程序中实现的任何蒙特卡罗方法的先决条件。因此，确定一个好的随机数生成器对于保证蒙特卡罗方法的输出质量很重要。然而，通过算法生成的数字序列并不是真正的随机，但对其随机性有一定的控制，本质上使它们成为伪随机的。最重要的是，具有概率分布的物理变量的模拟需要具有由算法本身生成的相同分布。从这个角度来看，考虑到“测量数据的评估——“测量不确定度表达指南”的补充 1——使用蒙特卡罗方法传播分布”中给出的量块校准示例，我们探讨了三种常用随机数生成器的属性和输出，即线性同余 (LC) 生成器、Wichmann-Hill (WH) 生成器和 Mersenne-Twister (MT) 生成器。广泛的测试表明，MT 算法的性能超越了 LC 和 WH 生成器的性能，尤其是在执行时间方面。此外，这些生成器用于估计长度测量中的不确定性，输入变量具有不同的概率分布。虽然在传统的 GUM 方法中，输出分布看起来像高斯分布，但我们从 Monte-Carlo 计算中发现它是学生的 t 分布。将 Welch-Satterthwaite 方程应用于 Monte Carlo 模拟的结果，我们发现有效自由度为 16。 另一方面，使用试错拟合方法来确定输出 PDF 的性质，我们发现结果分布是具有 46 个自由度的 t 分布。扩展这些结果以计算扩展的不确定性，我们发现蒙特卡罗结果与最近提出的基于均值/中值的无偏估计器一致，该估计器考虑了变换失真的伪影。