When Outliers Are Different
arXiv:2106.05212 · doi:10.1093/mnras/stab2551
Abstract
When does the presence of an outlier in some measured property indicate that the outlying object differs qualitatively, rather than quantitatively, from other members of its apparent class? Historical examples include the many types of supernovæ and short {\it vs.\/} long Gamma Ray Bursts. There may be only one parameter and one outlier, so that principal component analyses are inapplicable. A qualitative difference implies that some parameter has a characteristic scale, and hence its distribution cannot be a power law (that can have no such scale). If the distribution is a power law the objects differ only quantitatively. The applicability of a power law to an empirical distribution may be tested by comparing the most extreme member to its next-most extreme. The probability distribution of their ratio is calculated, and compared to data for stars, radio and X-ray sources, and the fluxes, fluences and rotation measures of Fast Radio Bursts. It is found with high statistical significance that the giant outburst of soft gamma repeater SGR 1806-20 differed qualitatively from its lesser outbursts and FRB 200428 differed qualitatively from other FRB (by location in the Galaxy), but that in some supernova remnant models of rotation measure FRB 121102 is not, statistically significantly, an outlier.
5 pp, 2 figs
References in corpus (17)
- A fast radio burst associated with a Galactic magnetar
- A bright millisecond-duration radio burst from a Galactic magnetar
- An exceptionally bright flare from SGR1806-20 and the origins of short-duration gamma-ray bursts
- Gamma-Ray Observations of a Giant Flare from The Magnetar SGR 1806-20
- FRBCAT: The Fast Radio Burst Catalogue
- Highest-frequency detection of FRB 121102 at 4-8 GHz using the Breakthrough Listen Digital Backend at the Green Bank Telescope
- Fast Radio Burst 121102 Pulse Detection and Periodicity: A Machine Learning Approach
- A Multi-telescope Campaign on FRB 121102: Implications for the FRB Population
- Statistical properties of SGR 1806-20 bursts
- Implications of a "Fast Radio Burst" from a Galactic Magnetar
- Rotation Measure Evolution of the Repeating Fast Radio Burst Source FRB 121102
- FRB event rate counts I --- Interpreting the Observations
- Implications of a rapidly varying FRB in a globular cluster of M81
- Two years of INTEGRAL monitoring of the Soft Gamma-Ray Repeater SGR 1806-20: from quiescence to frenzy
- Super-giant pulses from the Crab pulsar : Energy distribution and occurrence rate
- A universal energy distribution for FRB 121102
- FRB Strength Distribution Challenges the Cosmological Principle