Congruential Generators

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Congruential Generators

Congruential generators are based on relation with m,n and $\nu \protect$ non-negative integers,

$\nu \protect$ = n mod m

Subsections

which defines $\nu \protect$ as being congruent to n modulo m. It means that $\nu \protect$ is the remainder
Provided an initial seed $\nu _{0}\protect$ is supplied, a string of distinct values can be generated.
By taking $\xi _{i}=\nu _{i}/m\protect$ we find a sequence of numbers distributed on [0,1].
In the linear congruential generator, only one previous random variable is used to derive the next one, we can use more of the earlier generated numbers, each associated with a specified multiplier - a compound generator. If the last k generated numbers are used, we can write
where $n^{(i-1)}=(\nu _{i-1},\nu _{i-2},...,\nu _{i-k})\protect$ and the set of multipliers is a= (a $_{1},\protect$ a $_{2}\protect$ ,..,a $_{k}\protect$ ). By taking a value of just 2 for k and suitable multipliers a $_{1}\protect$ and a $_{2}\protect$ , a compound generator with acceptable result structure can be obtained, described next.

Amaury LATAILLADE 2002-11-04