Simulating pseudo random numbers
Pseudo random numbers are the basis for almost any statistical (Monte Carlo) simulation, and they are used in a huge variety of problems in statistics. Simulating them well is crucial for valid outputs on Monte Carlo simulations, and also resampling methods rely on the quality of pseudo random numbers.
We can distinguish between (at least) two kinds of pseudo random number generators:
- Arithmetic random number generators: They are based purely on, as the name suggests, arithmetic. Irrational numbers like
and e may be used as random number generators by making use of the fractional part of any multiples used. However, it is difficult to determine whether irrational numbers, as yet, have a periodicity. In addition, irrational numbers can only be presented as (finite) machine numbers in a computer; irrational numbers are rarely used in practice to generate random numbers.
- Recursive arithmetic random number generators: They are based on the calculation of a new...
