What is the Advantage of Using a Gaussian Distribution of Noise in a System?

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Discussion Overview

The discussion centers around the advantages of using a Gaussian distribution of noise in systems, particularly in the context of random number generation and its implications in simulations and stochastic processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the advantages of Gaussian noise compared to other distributions, seeking clarification on its unique properties.
  • Another participant suggests that Gaussian distribution is representative of actual random noise, implying a natural occurrence in real-world scenarios.
  • A participant raises a scenario involving the insertion of random numbers between 1 and 100, questioning the assertion that a Gaussian distribution would apply in this context.
  • In response, another participant clarifies that while each number is equally likely, the variation around the mean in a large sample size will follow a Gaussian distribution.
  • A later reply acknowledges the explanation regarding variation and expresses interest in further exploring stochastic processes and related topics.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Gaussian distribution to random number generation, with some agreeing on its relevance to variation around a mean, while others remain uncertain about its implications in specific scenarios.

Contextual Notes

There are unresolved questions regarding the relationship between random number distributions and Gaussian characteristics, as well as assumptions about the nature of randomness in the discussed scenarios.

Who May Find This Useful

Individuals interested in noise modeling, stochastic processes, probability theory, and those engaged in simulations or related projects may find this discussion relevant.

m~ray
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what is the advantage of using a gaussian distribution of noise (white/colored) in a system over any other distribution ??
 
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Do you mean other than the fact that this is what random noise actually looks like..?
 
Are you talking 'simulations'?
 
okay so u mean to say all random number distributions naturally follow the gaussian distribution?? say we need to insert 10^10 numbers between 1-100, where all the 100 places are equally likely to be filled. so eben in this case u mean to say on an avg there will be more number of numbers in 51 and 50?? if yes, then why should it be like that, as all numbers are equally likely to be filled..
 
No. Say you are picking numbers 1-100 completely at random, and you do this 10^10 times (This is the same as what you said, just phrased slightly differently). Now, the mean number of times you picked a given number will be 10^8 (10^10/100), but there will be some variation around this 10^8 mean and this variation will be described by a gaussian.
 
m~ray said:
okay so u mean to say all random number distributions naturally follow the gaussian distribution?? say we need to insert 10^10 numbers between 1-100, where all the 100 places are equally likely to be filled. so eben in this case u mean to say on an avg there will be more number of numbers in 51 and 50?? if yes, then why should it be like that, as all numbers are equally likely to be filled..
You are misinterpreting what the Gaussian distribution means, I think. Each number is equally likely: no more 50s than 99s. But it is more likely that adding any random two together will give an answer nearer to 100 than to 200 or 2. So it's the average and not the individual number that counts.
 
thanks a lot for the explanations. yes, the variation about the mean 10^8 describing a gaussian curve makes total sense now..

by the way, i am doing a project in stochastic resonance, and i want to learn more about stochastic processes, random numbers, probability theory, chaos and other related areas in the coming summer. Can u name me a few good books or other resources on such subjects?
 

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