The generation of high-quality randomness is a fundamental prerequisite for the integrity of stochastic modeling and numerical simulations across various scientific disciplines. As the complexity of computational experiments grows, the robustness of the underlying Pseudo-Random Number Generators (PRNGs) becomes a decisive factor in preventing systematic biases. This study examines the performance and reliability of PRNGs, focusing on the widely utilized Linear Congruential Generator (LCG) and the Combined Linear Congruential Generator (CLCG), which was developed to address the inherent limitations of the former. Using a simulation environment implemented in Python, both algorithms were evaluated based on visual distribution analysis (histograms and 2D/3D scatter plots), statistical fitness (Chi-Square and autocorrelation tests), and computational efficiency (execution speed). The empirical findings demonstrate that while the LCG operates approximately 2.1 times faster than the CLCG, it exhibits a distinct "lattice structure" in multi-dimensional space, leading to significant structural correlation errors. In contrast, the CLCG method, despite its higher computational overhead, achieved a high p-value of 0.92 in the Chi-Square goodness-of-fit test, indicating near-perfect alignment with the theoretical uniform distribution and minimized sequential dependency. Consequently, this study concludes that CLCG is a more reliable choice for high-precision simulations, whereas LCG remains viable for simple applications where computational speed is the primary constraint.
Eldoğan et al. (Thu,) studied this question.