In article <1210032721.26073.26.camel@[EMAIL PROTECTED]
>,
Christopher Battles <chris@[EMAIL PROTECTED]
> wrote:
> Good Evening,
>
> I'm trying to follow a paper from 1950 on the convolution of uniform
> distributions at:
>
>
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&h
> andle=euclid.aoms/1177729446
>
> Under section 2, they define the probability density of a uniform
> distribution as:
>
> f_i(x_i)=[epsilon(x_i) - epsilon(x_i - a_i)] / a_i
>
> (a_i > 0 ; i = 1,2,...,n)
> where epsilon(x - c) is unity for x >= c and zero elsewhere.
>
>
> I can't for the life of me see how this defines a uniform distribution??
> Any help in explaining this would be much appreciated.
So f_i(x_i) = 1/a_i if 0 <= x_i < a_i and is 0 elsewhere. That's a
uniform distribution. (The authors may have a reason for putting it in
this form.)
> Or, if anyone has a form for the convolution of n general uniform
> distributions that may be of a simpler form....
>
> I'm trying to compare the addition of a number of independent variables
> that follow a gaussian distribution with the same variables that follow
> a uniform distribution for an investigation into different error
> propagation techniques.
>
> Thank you all in advance,
>
> Christopher Battles
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