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I feel this question is trivial but I also couldn't find the answer (hope I am not bad at searching online). Put simply, I generate data from a normal distribution with mean=0 and standard deviation=1. Now, I want to inject noise into this dataset. to do so, I generate another set drawn from the normal distribution with the same mean but different standard deviation. Does that make sense?

Thank you,

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    $\begingroup$ Sure, then just add them together (or multiply them). But what exactly is your application? There are many ways to add noise to a data set, for example you could also use a different distribution. If you can provide more information people here can provide more help. $\endgroup$
    – user40845
    Jul 3, 2019 at 15:07
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    $\begingroup$ Even assuming normal distribution, depending on "how much" noise you want to add, you may prefer a different standard deviation $\endgroup$
    – David
    Jul 3, 2019 at 15:12
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    $\begingroup$ It will help immensely if you can expand on your goal. By simulating data from a distribution, you already have noise. $\endgroup$
    – Dave
    Feb 10, 2020 at 17:08
  • $\begingroup$ I've written a guide on adding noise to data. You can find it here: medium.com/@ms_somanna/… $\endgroup$
    – Somanna
    Aug 6, 2023 at 8:38

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Adding Gaussian noise is indeed a standard way of modeling random noise. Even in the case that the data itself is normally distributed. Of course other, and usually more complicated, noise models do exist, but this one is totally reasonable,

Just note that you might want to watch for ratio between the standard-deviations the data and the noise. The deviation of the noise should, on the basic scenarios, be signify lower or otherwise the noise might overcome the pattern within your data.

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