QQ Plots, Random Sets and Data from a Heavy Tailed Distribution

“…However, this slope functional is not necessarily continuous, as discussed in [6]. So consistency of the slope function requires further work and is an ongoing investigation.…”

Section: Introductionmentioning

confidence: 94%

A discussion on mean excess plots

Ghosh

Resnick

2010

Stochastic Processes and their Applications

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“…Then using the method of Das and Resnick [6] (Lemma 2.1. [18] , Das and Resnick [6] , Ghosh and Resnick [12] ). Thus,…”

Section: What If the Me Plot Converges?mentioning

confidence: 99%

When Does the Mean Excess Plot Look Linear?

Ghosh

Resnick

2011

Stochastic Models

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In risk analysis, the mean excess plot is a commonly used exploratory plotting technique for confirming iid data is consistent with a generalized Pareto assumption for the underlying distribution since in the presence of such a distribution, thresholded data have a mean excess plot that is roughly linear. Does any other class of distributions share this linearity of the plot?Under some extra assumptions, we are able to conclude that only the generalized Pareto family has this property.

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“…A Q-Q plot is commonly used for comparing a data set to a theoretical model and is a robust graphical method of distribution analysis (e.g. Fisher 1983;Evans et al 2000;Rosenkrantz 2000;Das & Resnick 2008). It is also used in astronomical data interpretation (e.g.…”

Section: Testing Of Normalitymentioning

confidence: 99%

Optical-radio positional offsets for active galactic nuclei

Orosz

Frey²

2013

A&A

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Context. It will soon become possible to directly link the most accurate radio reference frame with the Gaia optical reference frame using many common extragalactic objects. It is important to know the level of coincidence between the radio and optical positions of compact active galactic nuclei (AGNs). Aims. Using the best catalogues available at present, we investigate how many AGNs with significantly large optical-radio positional offsets exist as well as the possible causes of these offsets. Methods. We performed a case study by finding optical counterparts to the International Celestial Reference Frame (ICRF2) radio sources in the Sloan Digital Sky Survey (SDSS) Data Release 9 (DR9). The ICRF2 catalogue was used as a reference because the radio positions determined by Very Long Baseline Interferometry (VLBI) observations are about two orders of magnitude more accurate than the optical positions. Results. We find 1297 objects in common for ICRF2 and SDSS DR9. Statistical analysis of the optical-radio differences verifies that the SDSS DR9 positions are accurate to ∼55 milliarcseconds (mas) in both right ascension and declination, with no systematic offset with respect to ICRF2. We find 51 sources (∼4% of the sample) for which the positional offset exceeds 170 mas (∼3σ). Astrophysical explanations must exist for the majority of these outliers. There are three known strong gravitational lenses among them. Dual AGNs or recoiling supermassive black holes may also be possible. Conclusions. The most accurate Gaia-VLBI reference frame link will require a careful selection of a common set of objects by eliminating the outliers. On the other hand, the significant optical-radio positional non-coincidences may offer a new tool for finding e.g. gravitational lenses or dual AGN candidates. Detailed follow-up radio interferometric and optical spectroscopic observations are encouraged to investigate the outlier sources found in this study.

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QQ Plots, Random Sets and Data from a Heavy Tailed Distribution

Cited by 30 publications

References 13 publications

A discussion on mean excess plots

A discussion on mean excess plots

When Does the Mean Excess Plot Look Linear?

Optical-radio positional offsets for active galactic nuclei

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