On the Circular Median Absolute Deviation

The concentration of a circular distribution is typically measured through its mean resultant length, which also gives rise to the so-called circular variance. However, such a measure is not robust and contamination can affect its value, at least in the standardized bias sense. Alternative robust measures of spread are not available, especially if we distinguish between robust and robust versions of non-robust measures. For this reason, this work aims at evaluating a robust measure of spread: the Circular Median Absolute Deviation (Circular MAD). That is, the (linear) median of the distribution of the shortest arc distances from the circular median. Although its linear analog is one of the best available measures of scale in terms of robustness (the linear MAD achieving the highest possible breakdown point), we observe that the Circular MAD has been quite neglected within the literature so far. Neither its properties and behaviour under different scenarios, nor its link with any distribution are found in the literature. This work will partially fill this gap.