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Combined Linear Congruential Generator
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Combined Linear Congruential Generator : ウィキペディア英語版
Combined Linear Congruential Generator
A Combined Linear Congruential Generator (CLCG) is a pseudo-random number generator algorithm based on combining two or more linear congruential generators (LCG). A traditional LCG has a period which is inadequate for complex system simulation.〔Banks 2010, Sec. 7.3.2〕 By combining two or more LCGs, random numbers with a longer period and better statistical properties can be created.〔Banks 2010, Sec. 7.3.2〕
The algorithm is defined as:〔L'Ecuyer 1988〕
: X_i \equiv \left( \sum_^k (-1)^Y_ \right)\pmod
where:
: m_1 — the "modulus" of the first LCG
: Y_ — the ith input from the jth LCG
: X_i — the ith generated random integer
with:
: R_i \equiv \begin
X_i/m_1 & \text X_i > 0 \\
(m_1-1)/m_1 & \text X_i=0
\end

where R_ is a uniformly distributed random number between 0 and 1.
== Derivation ==
If ''W''''i'',1, ''W''''i'',2, ..., ''W''''i'',k are any independent, discrete, random-variables and one of them is uniformly distributed from 0 to ''m''1 − 2, then ''Z''''i'' is uniformly distributed between 0 and ''m''1 − 2, where:〔L'Ecuyer 1988〕
: Z_i= \left( \sum_^k W_ \right) \pmod
Let ''X''''i'',1, ''X''''i'',2, ..., ''X''''i'',''k'' be outputs from ''k'' LCGs. If ''W''''i'',''j'' is defined as ''X''''i'',''j'' − 1, then ''W''''i'',''j'' will be approximately uniformly distributed from 0 to ''m''''j'' − 1.〔L'Ecuyer 1988〕 The coefficient "(−1)''j''−1" implicitly performs the subtraction of one from ''X''''i'',''j''.〔Banks 2010, Sec. 7.3.2〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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