Random number

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The result of special random experiments is called a random number .

Random numbers are required in various statistical methods , e.g. B. when selecting a sample from a population , with the random distribution of test animals to different test groups ( randomization ), with the Monte Carlo simulation and the like. a.

There are various methods for generating random numbers. These are called random number generators . A decisive criterion for random numbers is whether the result of the generation can be viewed as independent of previous results or not.

Real random numbers and pseudo-random numbers

Real random numbers are generated with the help of physical phenomena: coin tossing, dice, roulette , noise from electronic components, radioactive decay processes or quantum physical effects. These methods are called physical random number generators , but are very time-consuming or technically complex.

In real applications, a sequence of pseudo- random numbers is often sufficient, i.e. seemingly random numbers that are generated using a fixed, reproducible process. So they are not random because they can be predicted, but they have similar statistical properties (even frequency distribution , low correlation ) as real random number sequences. Such procedures are called pseudo random number generators .

For other purposes, e.g. B. when generating cryptographic keys, however, real random numbers are required.

Standard random numbers

Standard random numbers should be able to be regarded as the realization of independent , uniformly distributed random variables .

One method for generating such sequences is called a standard random number generator. Such generators should be fast and the sequences generated should be easily reproducible in a straightforward manner. Most standard random number generators are congruence generators .

The simulation lemma enables, at least in principle, the generation of random numbers from other univariate distributions from standard random numbers with the aid of the inversion method .

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