Date: Mar 20, 2013 3:55 PM
Author: RGVickson@shaw.ca
Subject: Re: simple statistics question

On Wednesday, March 20, 2013 3:45:21 AM UTC-7, Thomas Plehn wrote:
> while(1) %Matlab code
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>
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> rr = rand(1,50); %sequence of 50 U(0,1) Values
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> des = rand(1,50); %sequence of 50 U(0,1) Values
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> diff = rr - des;
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> %This are both decide statistics, a, b
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> a = mean(rr);
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> b = min(diff);
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> disp(a-b); %their difference is nearly constant
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> %but how is it distributed (mu,sigma)
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> %and how does that depend on sequence length (n=50)
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> %i think we can chose U(0,1) insted of U(a,b) without los of generality
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> %(linear transformation of coordinates)
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>
>
> end


In plain English, is the following a description of your problem? (Below, I have changed the notation, and assigned different symbols from yours. However, if I understand correctly what you want, the concepts are the same.)

We take two independent samples X = (X_1,X_2,...,X_n) and Y = (Y_1,Y_2,...,Y_n) from the distribution U(0,1). [n = 50 in your case.] You take the difference sequence Z = (X_1-Y_1, X_2-Y_2,...,X_n-Y_n) and compute a = mean(X), b = min(Z) = smallest of the differences X_i - Y_i. Finally, you look at D = a - b. You want the mean and variance of D, and maybe also the actual distribution.

You claim that D is "almost constant", by which I assume you do the above computations many times, using many different samples, and come up with results that differ by little.

Is all that a fair summary of what you are trying to say?