It's not one that comes up much, so I looked it up: 

https://en.m.wikipedia.org/wiki/Bates_distribution


On Fri 13 Jul 2018 at 00:07, Jim Andrews <jim@vispo.com> wrote:
My bad, Antoine, James.

I wrote some code to look at the graph: http://vispo.com/temp/random.htm

You were right, Antoine, that the higher the number of random variables
averaged, the closer it is to the Normal or Gaussian distribution.

I was wrong that the average of two uniformly distributed variables is
Normally distributed.

I was right, however, that as you increase the number of random
variables, you change the standard deviation.

What is the name for the distribution, James, when you average two
uniformly distributed random vars? It's a pyramid-shaped graph.

ja


On 7/12/2018 11:19 AM, James McDermott wrote:
> No, Jim is totally wrong!
>
> The distribution of the sum of two uniform variables each in [0, 1] is not Gaussian. There are many distributions that look like a bell curve without being Gaussian (if you've heard of fat tails and black swans, this is related to that). But this one isn't even bell-shaped: it doesn't have support outside [0, 1].
>
> The lesson is as already noted: if getting it right matters, don't write your own statistics code, just use a good library.
>
> But perhaps more important: if you're getting results you like, it might not matter whether you understand your code in this way.
>
> James
>
>
>> On 12 Jul 2018, at 18:35, Antoine Schmitt <as@gratin.org> wrote:
>>
>> You are totally right.. My wrong.. ;)
>>
>>
>>> Le 12 juil. 2018 à 18:35, Jim Andrews <jim@vispo.com> a écrit :
>>>
>>> Hey Antoine. Great to hear from you. Thanks for the analysis and link.
>>>
>>> In the code of mine you quote, below, I would say that as one increases the number of (uniformly distributed) random variables xi, what changes is the standard deviation of what is already a Normal (or Gaussian) distribution. That is, as the number of averaged random variables increases, the tighter the clustering around the 0.5 mean.
>>> In other words, even when we average only 2 uniformly distributed random variables, the distribution is Normal (or Gaussian). What changes is not that it gets closer to a Normal distribution but, instead, it is already a Normal distribution, and what we change is the standard deviation, the tightness of the clustering around the mean.
>>>
>>> And I think that makes intuitive sense. If we compute the averages of a whole big bunch of uniformly distributed random variables, like a hundred of them, we will obviously almost always get a value really really close to 0.5. Whereas when we use just two random variables, as below in the first example, we are still going to get a 'bell' shaped curve over time, but there will be more frequent deviation from the 0.5 mean toward the left extremity of 0 and the right extremity of 1.
>>>
>>> ja
>>>
>>> On 7/12/2018 8:49 AM, Antoine Schmitt wrote:
>>>> This method is the way to approximate a gaussian distribution.
>>>> https://en.wikipedia.org/wiki/Normal_distribution
>>>> The higher the number of additions, the closer to the gaussian distribution you get.
>>>>
>>>>
>>>>> Le 11 juil. 2018 à 02:18, Jim Andrews <jim@vispo.com> a écrit :
>>>>>
>>>>> For instance,
>>>>>
>>>>> x1 = Math.random();
>>>>> x2 = Math.random();
>>>>> x3 = (x1 + x2)/2;
>>>>>
>>>>> Both x1 and x2 are random nums between 0 and 1. So too is x3. But x3 has a different distribution than x1 or x2. x3 has values around 0.5 more frequently than it has values around any other number.
>>>>>
>>>>> x1 = Math.random();
>>>>> x2 = Math.random();
>>>>> x3 = Math.random();
>>>>> x4 = (x1 + x2 + x3)/3;
>>>>>
>>>>> And in the above, x4 is yet more tightly clustered around 0.5
>>>>>
>>>>
>>>>
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Dr. James McDermott
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D209 UCD Michael Smurfit Graduate Business School
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