Statistically, random numbers exhibit no predictable pattern or regularity. Sequences of statistically random numbers are used to simulate complex mathematical and physical systems.
Random number generators can be used to approximate a random integer from a uniform distribution. When generated by a machine, these numbers are pseudorandom, which means they are deterministic and can be replicated in the same sequence. This allows for the ability to recreate an experiment or simulation with repeatable results, typically by specifying the algorithm as well as starting seeds.
Many types of Monte Carlo simulations require sequences that approximate other parametric or nonparametric distributions. Some common probability distributions include: