Why do weights in a weighted average have to be positive?
In the various pages I found in a Google search, i.e., Wikipedia, etc .. in defining weights they all specified that the weights must be non-negative.I'm not sure there's any "law" against using negative weights. How would you interpret a negative weight?
If you want to weight the contributions of items in some kind of compilation in terms of the magnitude of profit or loss, I see no reason why you couldn't do that. Essentially just summing over negative and positive numbers does exactly that. Quoting the Wiki needs to be done with care. It's context specific and not always reliable. Technically, calculating the mean or average can be an issue for mathematical types because you can get a sum of zero which you then must divide by the number of values less 1 to get the mean. However, meteorologists deal with negative temperature values all the time and are able to calculate means.In the various pages I found in a Google search, i.e., Wikipedia, etc .. in defining weights they all specified that the weights must be non-negative.
Weights are used in non probabilistic contexts such as averaging over ordered categorical data where the numbers in each category vary. It might be useful to give signed weights based on whether the category is seen as enhancing or detracting in some evaluative context.Weights are usually associated with probabilities, which is why I don't believe they can be negative. The number you are weighting, can of course be negative.