Iman Conover WS

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The Iman Conover approach is a good method to generate correlated numbers.

The original paper by Iman and Conover you can find here.

Stephen J. Mildenhall published a very good paper on this approach here.

I created an Excel © file following the example given in Mildenhalls paper:

The input matrix X:

The intermediate matrix M (constant values to to equal Mildenhalls data:

The target correlation S:

The Cholesky decomposition C of S:

You can create similar data automatically with array formula in A1:A20:

=NORMSINV(ROW(INDIRECT("1:20"))/21)/STDEVPA(NORMSINV(ROW(INDIRECT("1:20"))/21))

and with the array formula =randomshuffle(\$A\$1:\$A\$20) in cells B1:B20 (copy to columns C and D respectively).

Now you get the covariance matrix E:

And its Cholesky decomposition F:

The intermediate matrix T:

You can check the generated correlations:

Calculate the ranks of numbers in the columns of T: