# What is the difference between a Normal and a Gaussian Distribution

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.

Thanks

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Wikipedia is right, in this case. It usually is for topics like this. I would be more leery of it on controversial topics. –  Peter Flom Apr 12 '13 at 17:33
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. –  whuber Apr 12 '13 at 17:43
Go with Wikipedia & Peter & whuber - & hire a different private investigator. –  Scortchi Apr 12 '13 at 18:23
Here's one moderately authoritative reference: mathworld.wolfram.com/GaussianFunction.html. –  whuber Apr 12 '13 at 20:53
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. –  Glen_b Apr 12 '13 at 23:02

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

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The standard normal distribution is the standardIZED normal distribution. That means every value in the standard normal distribution is the z-score of a value in another normal distribution with non-normal mean and std.

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The wording is very confusing. In any case, it doesn't answer the the question at all. The comments have proved the answer. –  Student T Dec 18 '14 at 23:36
What on earth does this mean? –  Dilip Sarwate Dec 18 '14 at 23:36
Nevermind. I must have been tired. –  trsk Dec 30 '14 at 0:00

Actually the normal distribution is the sub form of Gaussian distribution. Gaussian distribution have 2 parameters, mean and variance. When there is zero mean and unit variance the Gaussian distribution becomes normal other wise it is pronounced as Gaussian.

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No. This is not right. The standard normal distribution has mean 0 and variance 1, but a normal distribution can have any mean and variance. –  Peter Flom Sep 5 '13 at 11:52