Are mixed LCG and combined LCG same thing?

[shivajikobardan]

Homework Statement

Linear Congruential Generators

Relevant Equations

Congruence equation

The whole problem arouse because there's no authentic local source. One thing that I need to learn is are these both same thing? Or are different? Is combined LCG also LCG or anything can be called combined method? Even our teachers aren't very sure of it(as they were not the ones who designed this curriculum or know the internal details of the course etc)

Is there any difference between "mixed Linear congruential generator" and "combined linear congruential generator". Are they same thing or different thing?

It's pretty confusing. No 2 books have explained about both topics. No books I've read yet, have talked about both of these.It's getting more confusing as I read more texts about it.

It says "mixed LCG" or "LCG" are the same thing.
https://www.cse.wustl.edu/~jain/iucee/ftp/k_26rng.pdf

https://www.eg.bucknell.edu/~xmeng/Course/CS6337/Note/master/node40.html

Optical Communication with Chaotic Lasers: Applications of Nonlinear Dynamics and Synchronization

Monte Carlo Methods in Financial Engineering

Jerry Banks

Molecular Modeling and Simulation: An Interdisciplinary Guide
By Tamar Schlick

This tells LCG and Mixed LCG is same thing in usage.

PROBABILITY AND STATISTICS - Volume II: Probabilistic Models and Methods ...
edited by Reinhard Viertl

Encyclopedia of Information Science and Technology, Fifth Edition
edited by Khosrow-Pour D.B.A., Mehdi

A Guide to Monte Carlo Simulations in Statistical Physics
By David Landau, Kurt Binder

Local source

Local source

local source

After reading these sources, it feels they're different but my local sources are confusing me. It feels LCGs are specifically just multiplicative and mixed. Whereas, combined Genrators doesn't necessarily named LCG.

 

[pbuk]

I am not going to read all of that, but I think all your questions are qickly answered by Wikipedia: https://en.wikipedia.org/wiki/Linear_congruential_generator

In short

• A linear congruential generator (LCG) has the form $x_{n+1} = (a x_n +c) \bmod m$.
• A mixed congruential generator is an LCG with $c \ne 0$ (edit: presumably because it has a 'mix' of a multiplicative and constant term).
• A multiplicative congruential generator (aka Lehmer RNG) is an LCC with $c = 0$ (edit because it only has a multiplicative term).
• A "Combined Linear Congruential Generator" is simply a combination of two or more LCGs: one example is the Wichmann Hill generator I see mentioned in one of your references; again wikipedia has more on these: https://en.wikipedia.org/wiki/Combined_linear_congruential_generator

I don't think this is the first time it has turned out that 10 minutes on Wikipedia would have been the best use of your time.

 

[shivajikobardan]

Thanks, I'll use wikipedia for confusions like this from now.