Formula Help --- G-Segregation Index

I am currently trying to use Excel to derive a G-segregation index, which is a form of the standard Gini coefficient.

The non-matrix form and matrix form equation for what I am trying to calculate is in the attached

I think this is the correct Excel formula for the numerator (as an array function), and it gives somehting which looks like the right result, but just wanted to check.

{=SUM(Y*TRANSPOSE(Y)*ABS(X-TRANSPOSE(X))}

Does anybody know if this is correct? Is there another way of calculating this?

[I would attach the original academic paper, bt don't want to infringe copyright - J.Silber - On the Measurement of Employment Segregation (1989)]

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