Is there a deep difference between a Normal and a Gaussian distribution, I've seen many papers using them without distinction, and I usually also refer to them as the same thing.

However, my PI recently told me that a normal is the specific case of the Gaussian with mean=0 and std=1, which I also heard some time ago in another outlet, what is the consensus on this?

According to Wikipedia, what they call the normal, is the standard normal distribution, while the Normal is a synonym for the Gaussian, but then again, I'm not sure about Wikipedia either.


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    $\begingroup$ Wikipedia is right, in this case. It usually is for topics like this. I would be more leery of it on controversial topics. $\endgroup$
    – Peter Flom
    Apr 12, 2013 at 17:33
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    $\begingroup$ There is a consensus. Your PI is confusing "Normal" with "Standard normal." The former refers to any version of the latter obtained via a change of location or scale. $\endgroup$
    – whuber
    Apr 12, 2013 at 17:43
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    $\begingroup$ Go with Wikipedia & Peter & whuber - & hire a different private investigator. $\endgroup$ Apr 12, 2013 at 18:23
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    $\begingroup$ Here's one moderately authoritative reference: mathworld.wolfram.com/GaussianFunction.html. $\endgroup$
    – whuber
    Apr 12, 2013 at 20:53
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    $\begingroup$ Peter Flom is right - as is Wikipedia, and whuber, and Scortchi. You can find any number of more authoritative works that support it - hundreds, perhaps thousands of standard texts for example and numerous papers. $\endgroup$
    – Glen_b
    Apr 12, 2013 at 23:02

3 Answers 3


Wikipedia is right. The Gaussian is the same as the normal. Wikipedia can usually be trusted on this sort of question.


In http://mathworld.wolfram.com/NormalDistribution.html, there is a mention of a standard Normal distribution which looks like the one you were mentioning as mean = 0 and std = 1. But the Normal distribution is the same as Gaussian which can be converted to a standard normal distribution by representing using the variable z = (x-mean)/std.


If you just talk about probability distribution, Gaussian and Normal distributions are identical as Wikipedia mentioned. But a Gaussian function is not necessarily a Normal distribution when its integrate is not to 1.

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    $\begingroup$ "But a Gaussian function is not necessarily a Normal distribution when its integrate is not to 1." This is not correct. All absolutely continuous probability distributions integrate to 1. This is part of how probabilities are conventionally defined (cf Kolmogorov axioms). $\endgroup$
    – Sycorax
    May 2, 2017 at 22:07
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    $\begingroup$ @Sycorax I think this may be in reference to the more generic "Gaussian function", which in some contexts need not be normalized (i.e. via a Gaussian integral factor). However I agree that the OP asked about a Gaussian distribution, so this answer is perhaps more of a comment. $\endgroup$
    – GeoMatt22
    May 3, 2017 at 1:13
  • $\begingroup$ "All absolutely continuous probability distributions integrate to 1" That is what I meant actually, should have said when the Gaussian function's integrate is not to 1 instead. $\endgroup$
    – Jerry
    May 3, 2017 at 16:49

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