Correct normalisation terminology Take the given values: -2.998, 8.0, 2.5.

My normalisation function takes a sum of the absolute values (13.498), let's call that x.

Next, each absolute value is divided by x (essentially calculating the mean distribution) - here's the result: 0.222, 0.593, 0.185.

So our result values are spread between 0-1, (it's what I need), and works great. But what's the precise terminology for this type of normalisation? I want to be able to document and comment my code accurately.
This is a bit unusual because you are throwing away information on the sign: The vectors (-2.998, 8.0, 2.5) and (2.9998, 8.0, 2.5) yield the same result.

Therefore I do not think there is a standard term for this procedure.
A clear comment in your code could be 'Take the absolut value and normalize by the sum of all values' or, if you are feeling mathematical today, 'Take the absolute value and normalize by the $L^1$-norm'.