The accepted pseudorandom number generators (PRNGs) having a (0,1) uniform distribution are tested to check if their behavior is really random. The “good” PRNGs must pass all imaginable tests.

This paper establishes a hierarchy of known PRNGs. The author analyses the accuracy of the pseudorandom number (PRN) sequences produced by a given PRNG. The quality of a random sequence is dependent on some local properties, such as the presence or absence of correlation among neighbor members of the generated random string. It is also determined by global properties of that sequence, which are related to the real multivariate distribution of the random elements of the string. Classifying PRNGs is difficult because the resulting random strings are dependent on the chosen generator seeds and on the sample volumes.

The author imagines a transformation of any (0,1) uniform random sequence into a discrete random sequence that has a known distribution. The proposed transformation is chosen so as to amplify the imperfections of the initial uniform (0,1) random string. Thus, the quality rankings of the studied PRNGs are given by the “good” properties of the transformed discrete random sequences. Since the theoretical distribution of these discrete sequences can be computed, the quality of any sequence is determined by the difference between the empirical and theoretical results concerning statistical functions of the sequence members.

The author applied the following comparison procedures: the chi-square test for goodness of fit, the approximation of a distribution by the normal distribution using a central limit theorem, and global comparison of the theoretical and empirical moments for the discrete random string obtained from the transformation. Using these interesting and practical techniques, the author effectively analyses more than 50 imposed PRNGs.