{'fraction_non_alphanumeric': 0.04713375796178344, 'fraction_numerical': 0.005095541401273885, 'mean_word_length': 5.390243902439025, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Random Number Generation and Quasi-Monte Carlo†

Probability theory defines random variables and stochastic processes in terms of probability spaces, a purely abstract notion whose concrete and exact realization on a computer is far from obvious. (Pseudo) random number generators (RNGs) implemented on computers are actually deterministic programs, which imitate to some extent, independent random variables uniformly distributed over the interval [0,1] (i.i.d. U[0,1], for short). RNGs are a key ingredient for Monte Carlo simulations, probabilistic algorithms, computer games, cryptography, casino machines, and so on. 
 
 
Keywords: 
 
random number generation; 
linear congruential generator; 
random variate generation; 
Monte Carlo; 
quasi-Monte Carlo; 
low-discrepancy sequence