It uses the positive and negative areas that are computed by ASSD-LL and the expected values of the prospects to compare them based on the ASSD-LL rule. If the violation area ratio is less than 0.5 for a prospect, and its expected value is larger, it dominates the other by ASSD-LL.
assd.ll.test(sd.obj)A list, including all the calculation details.
StochasticDominance object.
epsilon shows the ratio of the violation. Smaller epsilon means more decision-makers agree with the result.
The returned list has six elements: `winner` indicates the dominant prospect index. It will be zero if neither dominates the other. `epsilon` is the ratio of violated area to the total area between the CDFs. `area` is a vector, where the values show the area between the CDFs correspond to each segment. `total.area` is the total area between the CDFs. `positive.area` is the amount of area where the `area` vector is positive, meaning the `cdf1` is larger than `cdf2` and `ssd1` is larger than `ssd2`. `negative.area` is like `positive.area` for negative values.
If neither distribution dominates the other by ASSD-LL, the `winner` output will be zero, and it happens only when the distribution with a higher expected value has the `epsilon` which is larger than 0.5.
[expected.values(), pos.neg.area.assd.ll(), afsd.test()] for more details.