How to normalize data to 1 such that each value receives a weight proportional to their own value

Question

I have some data that do not sum to 1 that I would like to have sum to 1.

0.0232

0.05454

0.2154

0.5

0.005426

0.024354

0.00000456

sum: 0.82292456

I could just multiply each value by 1.0/0.82292456 and then have the sum be 1.00, but then all values would receive a factor adjustment of the same proportion (i.e 0.17707544).

I'd like to increase each value based on the size of the value itself. In other words, 0.5 would get a proportionally larger adjustment than 00000456 would.

I am not sure how to determine these adjustments that could potentially be additive, multiplicative, or both.

Any hints or suggestions would be helpful!

Thanks!

Answer 1

I could just multiply each value by 1.0/0.82292456 and then have the sum be 1.00, but then all values would receive a factor adjustment of the same proportion (i.e 0.17707544).

OK, That's what I'd do. Why is "a factor adjustment of the same proportion" a problem?

I'd like to increase each value based on the size of the value itself.

In that case, you should multiply each value by 1.0/0.82292456 because that's what multiplication does.