Contents

 
• Introduction
  • Outline and summary
  • Notations and concepts
  • Random Variables
    • Probability
    • The distribution of a random variable
    • Uniformity and independence
  • Random numbers
    • Pseudorandom numbers
    • Estimation techniques and the empirical distribution function
    • A sequence of independent uniform (pseudo-) RNs
  • Pseudorandom number generators
  • Structural properties of PRNGs
  • Summary: All random numbers are equal
• Tests for randomness
  • Stochastic simulation
  • Statistical tests
    • Theoretical tests
    • Empirical tests
    • Comparison
  • Posing the right questions
  • Summary: Some PRNs are more equal than others
• Empirical tests for uniform PRNs
  • A class of statistical tests for uniform PRNs
  • Test design
  • Interpretation of the results
  • PLAB
• Results
  • Bath-tub
  • Uncovering lattice structure
  • Inverse methods vs. linear methods
  • Summary: Different PRNGs and flexible tests
• The distribution of
  • The covariance matrix
  • The covariance matrix of
  • The multidimensional normal variate
  • Central limit theorems
  • The asymptotic distribution of
  • A generalized -test
  • A weak inverse for V
  • Putting the puzzle together
• Appendix
• References
• About this document ...

An dieser Stelle möchte ich mich bei all den Menschen bedanken, mit denen ich die letzten Jahre zusammensein und arbeiten durfte, und durch die ich jene Neugierde gelernt habe, welche die Mathematik erst zum Leben erweckt: Peter, Charly, Hannes, Otmar, Hrn. Thaler, Hrn. Österreicher, Hrn. Czermak, Doris und Roland.