MATLAB: Generate random numbers with specific properties

random numberspecific distribution

Is anyone aware of something within the Statistics Toolbox (or an FEX submission) that can generate a set of M random numbers where the mean of the random set is X and the mean of the absolute value of the random set is Y.
For example:
M = 21;
X = 0;
Y = 0.5;
A = some_rand_function(M,X,Y)
For example, a non-random version of A that almost matches the specific criteria is:
>> A = -1:0.1:1;
>> mean(A)
ans =
     0
>> mean(abs(A))
ans =
     0.528

Best Answer

Not all combinations (X,Y) will work of course. If you do not need a theoretical answer, and are content with something that might work, consider generating a sample any way you want, then trying to adjust it to fit your constraints:
>> X = 5;
>> Y = 7;
>> z = randn(100,1);
>> a = fminsearch(@(a) (X-mean(a(1)+a(2)*z))^2 + (Y-mean(abs(a(1)+a(2)*z)))^2,[5 5])
a =
    5.3484    7.4122
>> mean(a(1)+a(2)*z)
ans =
    5.0000
>> mean(abs(a(1)+a(2)*z))
ans =
    7.0000
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