# Deduction of Gauss' Normal Distribution Function

#### davidsousarj

Hello, I'm David. I'm a new member here.

Could anyone of you help me? Where can i find the formal deduction of Gauss' Normal Distribution Function? I've read a lot of statistics books and never found that. Where that comes from?

It's just curiosity, not homework.

P.S.: sorry about my english, I'm brazilian and my english is a little poor.

Related Set Theory, Logic, Probability, Statistics News on Phys.org

#### Stephen Tashi

Instead of "deduction", you may mean "derrivation". A derrivation would be a theorem of the form "If .... then the distribution has the following formula...." and the formula would be the one that is used for the gaussian distribution. The most famous theorem of this type is the Central Limit Theorem http://en.wikipedia.org/wiki/Central_limit_theorem .

If you are asking why the formula for the density for a gaussian distribution has the name "gaussian" or "normal", that's a historical question. There isn't any mathematical derrivation for it.

#### davidsousarj

Hi Stephen, thanks for the ansωer. I didn't knoω this theorem. Very interesting.

#### guicortei

Hi David.. I know this topic is very OLD (about 1.5 year), but when searching on google for exactly what you want, i was delivered to this forum... with no answer... so I kept searching and I found the derivation... you can find it here:

http://www.planetmathematics.com/DerNorm.pdf

P.S.: sorry about my english, I'm brazilian too.

#### davidsousarj

thanks, guicortei.

#### skanskan

The central limit theorem says that the arithmetic mean of a sufficiently large number of iterates of independent random variables will be approximately normally distributed,
but that doesn't derive the normal distribution equation in general.

And the pdf, just derives (again) an equation for a particular problem.

http://www.ams.org/journals/tran/1922-024-02/S0002-9947-1922-1501218-2/S0002-9947-1922-1501218-2.pdf

But I can't demostrate is that in a experiment the measures follow that distribution.

#### skanskan

You can also derive the normal distribution as the limit of the binomial one.

Gold Member
2018 Award

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving