446 research outputs found
On the Correct Use of Statistical Tests: Reply to "Lies, damned lies and statistics (in Geology)"
In a Forum published in EOS Transactions AGU (2009) entitled "Lies, damned
lies and statistics (in Geology)", Vermeesch (2009) claims that "statistical
significant is not the same as geological significant", in other words,
statistical tests may be misleading. In complete contradiction, we affirm that
statistical tests are always informative. We detail the several mistakes of
Vermeesch in his initial paper and in his comments to our reply. The present
text is developed in the hope that it can serve as an illuminating pedagogical
exercise for students and lecturers to learn more about the subtleties,
richness and power of the science of statistics.Comment: 7 pages and 1 figure: This text expands considerably the short text
published under the same title in Eos Transactions AGU, Vol. 92, No. 8, page
64, 22 February 201
Rigorous statistical detection and characterization of a deviation from the Gutenberg-Richter distribution above magnitude 8 in subduction zones
We present a quantitative statistical test for the presence of a crossover c0
in the Gutenberg-Richter distribution of earthquake seismic moments, separating
the usual power law regime for seismic moments less than c0 from another faster
decaying regime beyond c0. Our method is based on the transformation of the
ordered sample of seismic moments into a series with uniform distribution under
condition of no crossover. The bootstrap method allows us to estimate the
statistical significance of the null hypothesis H0 of an absence of crossover
(c0=infinity). When H0 is rejected, we estimate the crossover c0 using two
different competing models for the second regime beyond c0 and the bootstrap
method. For the catalog obtained by aggregating 14 subduction zones of the
Circum Pacific Seismic Belt, our estimate of the crossover point is log(c0)
=28.14 +- 0.40 (c0 in dyne-cm), corresponding to a crossover magnitude mW=8.1
+- 0.3. For separate subduction zones, the corresponding estimates are much
more uncertain, so that the null hypothesis of an identical crossover for all
subduction zones cannot be rejected. Such a large value of the crossover
magnitude makes it difficult to associate it directly with a seismogenic
thickness as proposed by many different authors in the past. Our measure of c0
may substantiate the concept that the localization of strong shear deformation
could propagate significantly in the lower crust and upper mantle, thus
increasing the effective size beyond which one should expect a change of
regime.Comment: pdf document of 40 pages including 5 tables and 19 figure
Characterization of the frequency of extreme events by the Generalized Pareto Distribution
Based on recent results in extreme value theory, we use a new technique for
the statistical estimation of distribution tails. Specifically, we use the
Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for
peak-over-threshold values in the form of the Generalized Pareto Distribution
(GPD). Useful in finance, insurance, hydrology, we investigate here the
earthquake energy distribution described by the Gutenberg-Richter seismic
moment-frequency law and analyze shallow earthquakes (depth h < 70 km) in the
Harvard catalog over the period 1977-2000 in 18 seismic zones. The whole GPD is
found to approximate the tails of the seismic moment distributions quite well
above moment-magnitudes larger than mW=5.3 and no statistically significant
regional difference is found for subduction and transform seismic zones. We
confirm that the b-value is very different in mid-ocean ridges compared to
other zones (b=1.50=B10.09 versus b=1.00=B10.05 corresponding to a power law
exponent close to 1 versus 2/3) with a very high statistical confidence. We
propose a physical mechanism for this, contrasting slow healing ruptures in
mid-ocean ridges with fast healing ruptures in other zones. Deviations from the
GPD at the very end of the tail are detected in the sample containing
earthquakes from all major subduction zones (sample size of 4985 events). We
propose a new statistical test of significance of such deviations based on the
bootstrap method. The number of events deviating from the tails of GPD in the
studied data sets (15-20 at most) is not sufficient for determining the
functional form of those deviations. Thus, it is practically impossible to give
preference to one of the previously suggested parametric families describing
the ends of tails of seismic moment distributions.Comment: pdf document of 21 pages + 2 tables + 20 figures (ps format) + one
file giving the regionalizatio
Robust statistical tests of Dragon-Kings beyond power law distributions
We ask the question whether it is possible to diagnose the existence of "Dragon-Kingsā (DK), namely anomalous observations compared to a power law background distribution of event sizes. We present two new statistical tests, the U-test and the DK-test, aimed at identifying the existence of even a single anomalous event in the tail of the distribution of just a few tens of observations. The DK-test in particular is derived such that the p-value of its statistic is independent of the exponent characterizing the null hypothesis, which can use an exponential or power law distribution. We demonstrate how to apply these two tests on the distributions of cities and of agglomerations in a number of countries. We find the following evidence for Dragon-Kings: London in the distribution of city sizes of Great Britain; Moscow and St-Petersburg in the distribution of city sizes in the Russian Federation; and Paris in the distribution of agglomeration sizes in France. True negatives are also reported, for instance the absence of Dragon-Kings in the distribution of cities in German
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