Data rescale question

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Data rescale question

Haijie Ding
Dear SPSS Listers,
I have a question regarding the data rescale. 
I have a list of variable (x1, x2, x3) which I want  to conduct linear combination to form a aggregated index(X). 
My first thought is to conduct standardized procedure for  x1, x2 and x3 and average the standardized scores. However, I realized and x1, x2 and x3 fit much better to power-law distribution than the normal distribution. And the means and stds are also very different from this variable to another. 
My question is: Can I still get the aggregated index for x1, x2 and x3? If the answer is yes, how should i do it?   (2) Is there any references I can get more /better understanding on this topic?

I really appreciate your kind reply. 

Bests,
Haijie