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1.
 Ad hoc techniques for estimating the position and the scale parameters of the Generalized Pareto distribution are introduced. The estimators proposed are simple linear combinations of the order statistics: they provide valuable estimates of the parameters of interest, both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications), and show a good performance as well when the sample size is small. The procedures are tested on simulated data, and comparisons with other techniques are shown.  相似文献   

2.
 Ad hoc techniques for estimating the position and the scale parameters of the Generalized Extreme Values distribution are introduced. The estimators proposed are simple linear combinations of the order statistics: they provide valuable estimates of the parameters of interest both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications), and show a good performance as well when the sample size is small. In addition, weakly-consistent estimators of the position parameter are introduced, whose calculation does not require the knowledge of any of the remaining parameters. The procedures are tested on simulated data, and comparisons with other techniques are shown.  相似文献   

3.
Recent results in extreme value theory suggest a new technique for statistical estimation of distribution tails (Embrechts et al., 1997), based on a limit theorem known as the Gnedenko-Pickands-Balkema-de Haan theorem. This theorem gives a natural limit law for peak-over-threshold values in the form of the Generalized Pareto Distribution (GPD), which is a family of distributions with two parameters. The GPD has been successfully applied in a number of statistical problems related to finance, insurance, hydrology, and other domains. Here, we apply the GPD approach to the well-known seismological problem of earthquake energy distribution described by the Gutenberg-Richter seismic moment-frequency law. We analyze shallow earthquakes (depth h<70 km) in the Harvard catalog over the period 1977–2000 in 12 seismic zones. The GPD is found to approximate the tails of the seismic moment distributions quite well over the lower threshold approximately M 1024 dyne-cm, or somewhat above (i.e., moment-magnitudes larger than m W =5.3). We confirm that the b-value is very different (b=2.06 ± 0.30) in mid-ocean ridges compared to other zones (b=1.00 ± 0.04) with a very high statistical confidence and propose a physical mechanism contrasting crack-type rupture with dislocation-type behavior. The GPD can as well be applied in many problems of seismic hazard assessment on a regional scale. However, in certain cases, deviations from the GPD at the very end of the tail may occur, in particular for large samples signaling a novel regime.  相似文献   

4.
In this study, the parameter estimations for the 3-parameter generalized logistic (GL) distribution are presented based on the methods of moments (MOM), maximum likelihood (ML), and probability weighted moments (PWM). The asymptotic variances of the MOM, ML, and PWM quantile estimators for the GL distribution are expressed as functions of the sample size, return period, and parameters. A Monte Carlo simulation was performed to verify the derived expressions for variances and covariances between parameters and to evaluate the applicability of the derived asymptotic variances of quantiles for the MOM, ML and PWM methods. The simulation results generally show good agreement with the analytical results estimated from the asymptotic variances of parameters and quantiles when the shape parameter (β) of the GL distribution is between −0.10 and 0.10 for the MOM method and between −0.25 and 0.45 for the ML and PWM methods, respectively. In addition, the actual sample variances and the root mean square error (RMSE) of asymptotic variances of quantiles for various sample sizes, return periods, and shape parameters were presented. In order to evaluate the applicability of the estimation methods to real data and to compare the values of estimated parameter, quantiles, and confidence intervals based on each parameter estimation method, the GL distribution was fitted to the 24-h annual maximum rainfall data at Pohang, Korea.  相似文献   

5.
Following a new train of thinking, this paper has explored first the potential information in the ground resistivity data observed by the existing geoelectric observation system, investigated and proposed a new dimensionless geoelectric precursor factor, the degree of ground resistivity anisotropy, S, and studied the characteristics of dynamic evolution pattern of S during the seismogenic process. The results show that, during the seismogenic process, the degree of ground resistivity anisotropy (S) displays a process of 'normal' →'abnormal strengthening (amplitude, range)' →abnormal weakening' → 'earthquake occurrence'→ 'normal'. The earthquake would occur at the time when the S value has entered the late stage of strengthening and turns to weaken and in the gradient belt on the margin of S anomaly region. The dynamic evolution pattern of S reflects the changes of the tectonic stress field during the seismogenic process. Therefore, it would be possible to trace the process of earthquake generation and occurrence from the dynamic evolution pattern of S so as to service earthquake prediction.  相似文献   

6.
In the present paper a statistical model for extreme value analysis is developed, considering seasonality. The model is applied to significant wave height data from the N. Aegean Sea. To build this model, a non-stationary point process is used, which incorporates apart from a time varying threshold and harmonic functions with a period of one year, a component μ w(t) estimated through the wavelet transform. The wavelet transform has a dual role in the present study. It detects the significant “periodicities” of the signal by means of the wavelet global and scale-averaged power spectra and then is used to reconstruct the part of the time series, μ w(t), represented by these significant features. A number of candidate models, which incorporate μ w(t) in their location and scale parameters are tried. To avoid overparameterisation, an automatic model selection procedure based on the Akaike information criterion is carried out. The best obtained model is graphically evaluated by means of diagnostic plots. Finally, “aggregated” return levels with return periods of 20, 50 and 100 years, as well as time-dependent quantiles are estimated, combining the results of the wavelet analysis and the Poisson process model, identifying a significant reduction in return level estimation uncertainty, compared to more simple non-stationary models.  相似文献   

7.
Heavy tailed random variables (rvs) have proven to be an essential element in modeling a wide variety of natural and human-induced processes, and the sums of heavy tailed rvs represent a particularly important construction in such models. Oriented toward both geophysical and statistical audiences, this paper discusses the appearance of the Pareto law in seismology and addresses the problem of the statistical approximation for the sums of independent rvs with common Pareto distribution F(x)=1 – x– for 1/2 < < 2. Such variables have infinite second moment which prevents one from using the Central Limit Theorem to solve the problem. This paper presents five approximation techniques for the Pareto sums and discusses their respective accuracy. The main focus is on the median and the upper and lower quantiles of the sums distribution. Two of the proposed approximations are based on the Generalized Central Limit Theorem, which establishes the general limit for the sums of independent identically distributed rvs in terms of stable distributions; these approximations work well for large numbers of summands. Another approximation, which replaces the sum with its maximal summand, has less than 10% relative error for the upper quantiles when < 1. A more elaborate approach considers the two largest observations separately from the rest of the observations, and yields a relative error under 1% for the upper quantiles and less than 5% for the median. The last approximation is specially tailored for the lower quantiles, and involves reducing the non-Gaussian problem to its Gaussian equivalent; it too yields errors less than 1%. Approximation of the observed cumulative seismic moment in California illustrates developed methods.  相似文献   

8.
On the basis of comparison of the approaches to the solution of inverse problems in information theory and geophysics, it is shown that results, obtained in information theory, are suitable to supplement the theory of geophysical inverse problems. The conditions of the existence and uniqueness of the solutions of inverse problems in their practical discrete statement are specified. The terms of ɛ-entropy H ɛ and informational capacity C ɛ, characterizing “volumes” of unknown and observed data, are introduced. It is shown, that the instability of the solution of the inverse problem decreases with increase in H ɛ, (increase in the “complexity” of studied section), if the relation H ɛ ≤ C ɛ is maintained.  相似文献   

9.
 Estimation of confidence limits and intervals for the two- and three-parameter Weibull distributions are presented based on the methods of moment (MOM), probability weighted moments (PWM), and maximum likelihood (ML). The asymptotic variances of the MOM, PWM, and ML quantile estimators are derived as a function of the sample size, return period, and parameters. Such variances can be used for estimating the confidence limits and confidence intervals of the population quantiles. Except for the two-parameter Weibull model, the formulas obtained do not have simple forms but can be evaluated numerically. Simulation experiments were performed to verify the applicability of the derived confidence intervals of quantiles. The results show that overall, the ML method for estimating the confidence limits performs better than the other two methods in terms of bias and mean square error. This is specially so for γ≥0.5 even for small sample sizes (e.g. N=10). However, the drawback of the ML method for determining the confidence limits is that it requires that the shape parameter be bigger than 2. The Weibull model based on the MOM, ML, and PWM estimation methods was applied to fit the distribution of annual 7-day low flows and 6-h maximum annual rainfall data. The results showed that the differences in the estimated quantiles based on the three methods are not large, generally are less than 10%. However, the differences between the confidence limits and confidence intervals obtained by the three estimation methods may be more significant. For instance, for the 7-day low flows the ratio between the estimated confidence interval to the estimated quantile based on ML is about 17% for T≥2 while it is about 30% for estimation based on MOM and PWM methods. In addition, the analysis of the rainfall data using the three-parameter Weibull showed that while ML parameters can be estimated, the corresponding confidence limits and intervals could not be found because the shape parameter was smaller than 2.  相似文献   

10.
ＯｎｓｏｍｅｐｒｏｂｌｅｍｓｏｆｓｅｉｓｍｉｃｃｒｕｓｔａｌｐｈａｓｅＨｕａｎ－ＣｈｅｎｇＧＥ（葛焕称）（ＳｅｉｓｍｏｌｏｇｉｃａｌＢｕｒｅａｕｏｆＪｉａｎｇｓｕＰｒｏｖｉｎｃｅ,Ｎａｎｊｉｎｇ２１００１４,Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...  相似文献   

11.
IntroductionIn the book Future CataS~ologr published in 1992, we proposed a viewpoiflt on using the"criterion of activity in quiescence" to predict big eathquake (MsZ7) (GUO, et al, 1992), and predicted in the book that in futore several years or in ten years a big earthquake (Ms27) will be possible to occur in the Zhongdian and nearby in Yunnan Province. In the 1994 nation-wide earthquake tendency consultation meeting we pointed out, once more, in the Zhongdian region of Yunnan Province…  相似文献   

12.
In this paper, one of the distribution-free tests — randomization test, is briefly described. It doesn’t need any distribution assumption and its related parameter estimation and is applicable to random and nonrandom sample. Then it is used to the test of migration of strong earthquakes on the Xianshuihe Fault Belt and “immunity” of large earthquakes in the large northern reigon of China. The test results show that there is 98.7% confidence degree for the migration of strong earthqueks on the Xianshuihe Fault Belt and “immunity” of earthqueks withM S⩾8 toM S⩾7 is significant in the large northern region of China. The obtained test results and the test method itself have certain application in the practice. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 484–489, 1993.  相似文献   

13.
Generous statistical tests   总被引：1，自引：1，他引：0  
A common statistical problem is deciding which of two possible sources, A and B, of a contaminant is most likely the actual source. The situation considered here, based on an actual problem of polychlorinated biphenyl contamination discussed below, is one in which the data strongly supports the hypothesis that source A is responsible. The problem approach here is twofold: One, accurately estimating this extreme probability. Two, since the statistics involved will be used in a legal setting, estimating the extreme probability in such a way as to be as generous as is possible toward the defendant’s claim that the other site B could be responsible; thereby leaving little room for argument when this assertion is shown to be highly unlikely. The statistical testing for this problem is modeled by random variables {X i } and the corresponding sample mean the problem considered is providing a bound ɛ for which for a given number a 0. Under the hypothesis that the random variables {X i } satisfy E(X i ) ≤ μ, for some 0  < μ < 1, statistical tests are given, described as “generous”, because ɛ is maximized. The intent is to be able to reject the hypothesis that a 0 is a value of the sample mean while eliminating any possible objections to the model distributions chosen for the {X i } by choosing those distributions which maximize the value of ɛ for the test used.  相似文献   

14.
In this paper, we show how to estimate the phase velocities of multi-mode signals as present in 2-D shallow seismic surveys along a seismic line with the help of a method that is based on the deformation of the wavelet spectra of the seismic traces. In analogy with frequency-wavenumber (f–k) analysis, we perform “frequency-velocity” analysis using the correlations between phases of the wavelet spectra. Our method has two tuning parameters — the parameter of an analyzing wavelet and the parameter of a threshold operation. Numerical and experimental examples are presented to illustrate how the method accurately extracts the phase velocity from single- and multi-mode signals.  相似文献   

15.
Conclusion Based on the analysis about the law of deformation rate, the concepts of the deformation rate of precursor, and its stress drop, and the stress drop of instability are discussed. According to the obtained deformationu 0 corresponding to the maximum stress, the unstable pointu 1 and the stable pointu 2 of equilibrium, the complete process of rock failure can be divided into four stages quantitatively, corresponding to “the steady stage I”, “the precursor stage II”, “the unstable stage III” and “the later stage IV” of rock failure respectively, which can be used to simulate the complete course of earthquake. This kind of similarity between the complete process of rock failure and the complete course of earthquake suggests clearly the direction to reveal the law being of universal significance for the simulation of the earthquake in the laboratory experiments. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 517–521, 1991.  相似文献   

16.
Two approaches for the modelling of turbulence in vegetated flows have been developed in the past. The “microscopic” approach which is straightforward but limited to simple cases and the “macroscopic” approach which is based on Volume Average Theory (VAT). In this study, aspects of Volume-Average (VA) analysis and modelling are investigated for turbulent vegetated flow using computed three-dimensional results from the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations around a representative vegetal element. In particular (a) the VA transport equations for k and ε, based on VAT, are properly derived, (b) the Boussinesq hypothesis for the VA quantities, employed in 〈k〉-〈ε〉 turbulence models is tested, and (c) the values of the coefficients used in such turbulence models are assessed in comparison with those used in the classical turbulence models.  相似文献   

17.
The bacterial community in deep subseafloor sediments at a depth of 230 cm from the western Pacific “warm pool” is studied by construction of 16S rDNA clone library and PCR-RFLP (Restriction Fragment Length Polymorphism) analysis. The results indicate that the bacterial community in these sediments is mainly composed of five groups: α-Proteobacteria, β-Proteobacteria, CFB group (Cytophaga / Flexibacteria / Bacteroides), Acidobacteria and gram positive bacteria, with a few genera detected in each group. The most abundant bacteria group is α-Proteobacteria, and the next is β-Proteobacteria. The dominant species in α-and β-Proteobacteria are Sphingomonas paucimobilis and Pseudomonas alcaligenes respectively. The CFB group is simply composed of members belonging to Flavobacterium. The gram positive bacteria are rich, and mainly consists of the genus Geobacillus. The analysis of bacterial community indicates that organic matter is still abundant in the subseafloor sediments at the depth of 230 cm in the western Pacific “warm pool”. These bacteria in this deep biosphere may play an important role in the nitrogen cycle of deep sea sediments at “warm pool”. Supported by the National Key Basic Research Support Foundation of China (Grant No. G2000078500) and China Ocean Mineral Resources R&D Association Project (Grant No. DY105-4-2-4)  相似文献   

18.
Summary The Lac de Bret, formerly an “oligotrophic” lake, has by several artificial risings of its level become “eutrophic” with the drawbacks of that state during the summer stagnation. A plant of partial underwater aeration has improved the situation and has been described in this Review (11, 423 [1949]). The above study compares the zooplancton of this lake in the years 1902/03 when it was yet oligotrophic with its plancton in the year 1943 during the investigations in the lake become eutrophic and finally in the year 1951 when it had again grown sound after five seasons of estival acration.   相似文献   

19.
Case histories of water level subsidence in bore-holes as a precursor of earthquakes are given here. Based on the examples, a testable quantitative theory for causative mechanism of the precursor—“draining-injecting water model with variable discharge” is proposed (abbreviated to DIW model). Through analysing the constitution law of which the deformation changes in the porous, water-saturated media under the effect of exterior stress, as first step of all, the authors suggested first a simple “drainage-natural restoration model” (abbreviated to DNR model), calculated and gave a group of theoretical precursor curve by using DNR model, compared the theoretical precursor curves of DNR model with the observational curves, found out the differences of the two curves, studied the causative physical factors that caused the differences then, revised the DNR model, and finally, the theory on “draining-injecting water model with variable discharge” in the paper was obtained. The authors deduced general equation of the two dimensions “draining-injecting water linear source drawdown field” in the paper, suggested and developed the concept on “domain”. DIW model can also give a possible explanation for both regularity and complexity of this precursor. DIW theory can quantitatively divide the seismogenic process of the foci on the short-term and impending process into several phases, and by inversing the discharge functionq(τ) curve, the time values by which the phases are divided were obtained. They will be helpful to predicting the occurrence time of earthquake and judging the DD and IPE model of the seismogenesis. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 194–201, 1993.  相似文献   

20.
Robustness of large quantile estimates to the largest element in a sample of methods of moments (MOM) and L-moments (LMM) was evaluated and compared. Quantiles were estimated by log-logistic and log-Gumbel distributions. Both are lower bounded and two-parameter distributions, with the coefficient of variation (CV) serving as the shape parameter. In addition, the results of these two methods were compared with those of the maximum likelihood method (MLM). Since identification and elimination of the outliers in a single sample require the knowledge of the samples parent distribution which is unknown, one estimates it by using the parameter estimation method which is relatively robust to the largest element in the sample. In practice this means that the method should be robust to extreme elements (including outliers) in a sample.The effect of dropping the largest element of the series on the large quantile values was assessed for various coefficient of variation (CV) / sample size (N) combinations. To that end, Monte-Carlo sampling experiments were applied. The results were compared with those obtained from the single representative sample, (the first order approximation), i.e., consisting of both the average values (Exi) for every position (i) of an ordered sample and the theoretical quantiles based on the plotting formula (PP).The ML-estimates of large quantiles were found to be most robust to largest element of samples except for a small sample where MOM-estimates were more robust. Comparing the performance of two other methods in respect to the large quantiles estimation, MOM was found to be more robust for small and moderate samples drawn from distributions with zero lower bound as shown for log-Gumbel and log-logistic distributions. The results from representative samples were fairly compatible with the M-C simulation results. The Ex-sample results were closer to the M-C results for smaller CV-values, and to the PP-sample results for greater CV values.  相似文献   

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