On the identification of Dragon Kings among extreme-valued outliers

Riva, Mònica; Neuman, Shlomo P.; Guadagnini, Alberto

doi:10.5194/npg-20-549-2013

Cited by 8 publications

(5 citation statements)

References 49 publications

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“…Heavy tails are important because they control the distributions of extreme values, which are of central interest in hydrology and many other fields [Katz et al, 2002;Riva et al, 2013c]. We propose a new statistical model that reconciles the behaviors of variables and increments possessing heavy-tailed distributions, the tails and peaks of which scale with lag in the above manner.…”

Section: Introductionmentioning

confidence: 97%

New scaling model for variables and increments with heavy‐tailed distributions

Riva

Neuman

Guadagnini

2015

Water Resources Research

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Many hydrological (as well as diverse earth, environmental, ecological, biological, physical, social, financial and other) variables, Y, exhibit frequency distributions that are difficult to reconcile with those of their spatial or temporal increments, DY. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of DY tend to be symmetric with peaks that grow sharper, and tails that become heavier, as the separation distance (lag) between pairs of Y values decreases. No statistical model known to us captures these behaviors of Y and DY in a unified and consistent manner. We propose a new, generalized sub-Gaussian model that does so. We derive analytical expressions for probability distribution functions (pdfs) of Y and DY as well as corresponding lead statistical moments. In our model the peak and tails of the DY pdf scale with lag in line with observed behavior. The model allows one to estimate, accurately and efficiently, all relevant parameters by analyzing jointly sample moments of Y and DY. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole.

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Section: Introductionmentioning

confidence: 97%

New scaling model for variables and increments with heavy‐tailed distributions

Riva

Neuman

Guadagnini

2015

Water Resources Research

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“…There is growing evidence that these frequency distributions, as well as other geospatial and/or temporal statistics of many data, vary with scale. A key related question concerns the scale dependence of frequency distributions (typically generalized extreme value or GEV in the case of block extrema and generalized Pareto distribution or GPD in the case of peaks over thresholds or POTs, e.g., Embrechts et al, 1997) and statistics of extremes at the tails of the original data distributions (e.g., Riva et al, 2013a).…”

Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

“…Our alternative interpretation of the data allows us to obtain maximum likelihood (ML) estimates of all parameters characterizing the underlying truncated subGaussian fields at both intra-and inter-layer scales. Most importantly, we offer what appears to be the first data-driven exploration (following a synthetic study of outliers by Riva et al, 2013a) of how statistics of POTs associated with such families of sub-Gaussian fields vary with scale.…”

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confidence: 99%

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Guadagnini

Neuman

Nan

et al. 2015

Hydrol. Earth Syst. Sci.

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Abstract. We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain lags. The phenomena we uncover are of key importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.

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“…To strengthen the evidence of the existence of such outliers, we performed a statistical test, aimed at assessing the confidence intervals of the possible deviations. Different statistical tests to detect outliers in a distribution have been proposed in the literature [1,26,[59][60][61][62]. Here, we used the one proposed by Janczura and Weron, based on the asymptotic properties of the empirical cumulative distribution function and the use of the central limit theorem (see Appendix B and Reference [26] for more details).…”

Section: Theoretical Resultsmentioning

confidence: 99%

Statistical outliers in random laser emission

et al. 2018

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We provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power-law tailed (Lévy) distribution. Such outliers manifest themselves as single, large isolated spikes over an otherwise smooth background. A statistical test convincingly shows that their probability is larger than the one extrapolated from lower-intensity events. To compare with experimental data, we introduced the anomaly parameter that allows for an identification of such rare events from experimental spectral measurements and that agrees as well with the simulations of our Monte Carlo model. A possible interpretation in terms of Black Swans or Dragon Kings, large events having a different generation mechanism from their peers, is discussed.

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On the identification of Dragon Kings among extreme-valued outliers

Cited by 8 publications

References 49 publications

New scaling model for variables and increments with heavy‐tailed distributions

New scaling model for variables and increments with heavy‐tailed distributions

Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

Statistical outliers in random laser emission

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