Once you abanndon independence, the possibilities are litteraly infinite—and not just easily controllable infinities, either. I worked with SD as that’s the simplest model I could use; but skewness, kurtosis or, Bayes help us, the higher moments, are also valid choices.
You just have to be careful that your choice of units is consistent; the SD and the mean are in the same unit, the variance is in units squared, the skewness and kurtosis are unitless, the k-th moment is in units to the power k, etc...
That’s true—and it occurred to me after I posted the comment that your criteria don’t define the decision system anyway, so even using some other method you might still be able to prove that it meets your conditions.
Once you abanndon independence, the possibilities are litteraly infinite—and not just easily controllable infinities, either. I worked with SD as that’s the simplest model I could use; but skewness, kurtosis or, Bayes help us, the higher moments, are also valid choices.
You just have to be careful that your choice of units is consistent; the SD and the mean are in the same unit, the variance is in units squared, the skewness and kurtosis are unitless, the k-th moment is in units to the power k, etc...
That’s true—and it occurred to me after I posted the comment that your criteria don’t define the decision system anyway, so even using some other method you might still be able to prove that it meets your conditions.