Generate random numbers with specific properties

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

Answer 1

[Tom Lane]

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

[Dr. Seis]

As one of my professors used to say, "Good enough for government work!"

Thanks, Tom!