Why doesn’t Radar Logic just use the data median?
There are a couple of big advantages to Triple Power Law parameterization over the raw data median. First, the data median can miss dynamics that are present only in a particular segment of the market. For example, if low-end prices are declining while the rest of the market is remaining stable, the median would largely ignore it since those transactions started and ended below the median, while the left slope of the Triple Power Law distribution would become less steep (and consequently the index price lower) to reflect that decline. A second major benefit is that a Triple Power Law approach does better in the presence of bad or idiosyncratic data since it does not blindly accommodate all datapoints but instead places them in a larger context. As a corollary, Triple Power Law provides a criterion for determining whether there are issues with the data, as in the example above of the normal distribution of heights and an irregular bump on the right tail resulting from the passage of the
