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1.
Expressions for the expected values of GEV order statistics have been derived in simple summation form and in terms of probability weighted moments. Using exact plotting positions from GEV order statistics a new unbiased plotting position formula has been developed for the General Extreme Value distribution. The formula can, explicitly, take into account the coefficient of skewness, (or the shape parameter, k), of the underlying distribution.The developed formula better approximates the exact plotting positions as compared to other existing formulae and is quite easy to use. 相似文献
2.
A new unbiased plotting position formula for Gumbel distribution 总被引：1，自引：0，他引：1
The probability plots (graphical approach) are used to fit the probability distribution to given series, to identify the
outliers and to assess goodness of fit. The graphical approach requires probability of exceedence or non exceedence of various
events. This is obtained through the use of plotting position formula. In literature many plotting position formulae have
been reported. All of the many existing formulae provide different results particularly at the tails of the distribution and
hence there is need of unbiased plotting position formulae for different distributions. Expression for the largest expected
order statistics is found in a simple form. Using exact plotting position from Gumbel order statistics a new unbiased plotting
position formula has been developed for the Gumbel distribution. The developed formula better approximates the exact plotting
positions as compared to other existing formulae. 相似文献
3.
A distribution free plotting position 总被引：6，自引：1，他引：6
G.-H. Yu C.-C. Huang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(6):462-476
Many plotting position formulae have been proposed for the past few decades. These formulae are derived or obtained under
some specific assumption of probability distribution. Because in practice the data are often plotted in order to determine
its probability distribution, it causes difficulty and confusion in selecting the plotting position formula. The objective
of this study is to find a plotting position formula which is distribution free. In this study, the plotting position formulae
corresponding to the order statistic mean, mode and median are investigated. The order statistic mean, mode and median values
are determined by numerical integration and differentiation, and the corresponding plotting position formulae are obtained
by regression analysis. The results indicate that both the plotting position formulae for the order statistic mean and mode
vary with the distribution of data, but the plotting position formula for the order statistic median is distribution free.
The distribution free plotting position formula for the order statistic median is proposed in this study as (i−0.326)/(n+0.348). 相似文献
4.
Applicability of Wakeby distribution in flood frequency analysis: a case study for eastern Australia 总被引：1，自引：0，他引：1 
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下载免费PDF全文 Ataur Rahman Mohammad A. Zaman Khaled Haddad Salaheddine El Adlouni Chi Zhang 《水文研究》2015,29(4):602-614
Parametric method of flood frequency analysis (FFA) involves fitting of a probability distribution to the observed flood data at the site of interest. When record length at a given site is relatively longer and flood data exhibits skewness, a distribution having more than three parameters is often used in FFA such as log‐Pearson type 3 distribution. This paper examines the suitability of a five‐parameter Wakeby distribution for the annual maximum flood data in eastern Australia. We adopt a Monte Carlo simulation technique to select an appropriate plotting position formula and to derive a probability plot correlation coefficient (PPCC) test statistic for Wakeby distribution. The Weibull plotting position formula has been found to be the most appropriate for the Wakeby distribution. Regression equations for the PPCC tests statistics associated with the Wakeby distribution for different levels of significance have been derived. Furthermore, a power study to estimate the rejection rate associated with the derived PPCC test statistics has been undertaken. Finally, an application using annual maximum flood series data from 91 catchments in eastern Australia has been presented. Results show that the developed regression equations can be used with a high degree of confidence to test whether the Wakeby distribution fits the annual maximum flood series data at a given station. The methodology developed in this paper can be adapted to other probability distributions and to other study areas. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
This paper considers a problem of analyzing temporal and spatial structure of particulate matter (PM) data with emphasizing high-level \(\text {PM}_{10}\). The proposed method is based on a combination of a generalized extreme value (GEV) distribution and a multiscale concept from scaling property theory used in hydrology. In this study, we use hourly \(\text {PM}_{10}\) data observed for 5 years on 25 stations located in Seoul metropolitan area, Korea. For our analysis, we calculate monthly maximum values for various duration times and area coverages at each station, and show that their distribution follows a GEV distribution. In addition, we identify that the GEV parameters of \(\text {PM}_{10}\) maxima hold a new scaling property, termed ‘piecewise linear scaling property’ for certain duration times. By using this property, we construct a 12-month return level map of hourly \(\text {PM}_{10}\) data at any arbitrary d-hour duration. Furthermore, we extend our study to understand spatio-temporal multiscale structure of \(\text {PM}_{10}\) extremes over different temporal and spatial scales. 相似文献
6.
We derive the current-voltage relationship in the auroral region taking into account magnetospheric electrons for the bi-Maxwellian and kappa source plasma distribution functions. The current-voltage formulas have in principle been well known for a long time, but the kappa energy flux formulas have not appeared in the literature before. We give a unified treatment of the bi-Maxwellian and kappa distributions, correcting some errors in previous work. We give both exact results and two kinds of approximate formulas for the current density and the energy flux. The first approximation is almost generally valid and is practical to compute. The first approximation formulas are therefore suitable for use in simulations. In the second approximation we assume in addition that the thermal energy is small compared to the potential drop. This yields even simpler linear formulas which are suitable for many types of event studies and which have a more transparent physical interpretation than the first approximation formulas. We also show how it is possible to derive the first approximation formulas even for those distributions for which the exact results can not be computed analytically. The kappa field-aligned conductance value turns out always to be smaller than the corresponding Maxwellian conductance. We also verify that the obtained kappa current density and energy flux formulas go to Maxwellian results when k . 相似文献
7.
The paper deals with the probability estimates of temperature extremes (annual temperature maxima and heat waves) in the Czech Republic. Two statistical methods of probability estimations are compared; one based on the stochastic modelling of time series of the daily maximum temperature (TMAX) using the first-order autoregressive (AR(1)) model, the other consisting in fitting the extreme value distribution to the sample of annual temperature peaks.The AR(1) model is able to reproduce the main characteristics of heat waves, though the estimated probabilities should be treated as upper limits because of deficiencies in simulating the temperature variability inherent to the AR(1) model. Theoretical extreme value distributions do not yield good results when applied to maximum annual lengths of heat waves and periods of tropical days (TMAX 30°C), but it is the best method for estimating the probability and recurrence time of annual one-day temperature extremes. However, there are some difficulties in the application: the use of the two-parameter Gumbel distribution and the three-parameter generalized extreme value (GEV) distribution may lead to different results, particularly for long return periods. The resulting values also depend on the chosen procedure of parameter estimation. Based on our findings, the shape parameter testing for the GEV distribution and the L moments technique for parameter estimation may be recommended.The application of the appropriate statistical tools indicates that the heat wave and particularly the long period of consecutive tropical days in 1994 were probably a more rare event than the record-breaking temperatures in July 1983 exceeding 40°C. An improvement of the probability estimate of the 1994 heat wave may be expected from a more sophisticated model of the temperature series. 相似文献
8.
Summary An exact solution of the distribution of the intensity of the telluric field in a halfspace with a spherical inhomogeneity has been obtained by solving the Laplace equation in bipolar coordinates. This exact solution is compared with the presently known approximate solution, obtained by the method of images, and the region of their coincidence has been determined. For the image solution theoretical relations have been derived for computing the anomaly of the magnetic field. Craphs depict many of the properties of the telluric and magnetic fields on the surface of the considered halfspace for various parameters of the given problem.Dedicated to 90th Birthday of Professor Frantiek Fiala 相似文献
9.
F. Ashkar B. Bobée D. Leroux D. Morisette 《Stochastic Environmental Research and Risk Assessment (SERRA)》1988,2(3):161-174
The generalized gamma (GG) distribution has a density function that can take on many possible forms commonly encountered in hydrologic applications. This fact has led many authors to study the properties of the distribution and to propose various estimation techniques (method of moments, mixed moments, maximum likelihood etc.). We discuss some of the most important properties of this flexible distribution and present a flexible method of parameter estimation, called the generalized method of moments (GMM) which combines any three moments of the GG distribution. The main advantage of this general method is that it has many of the previously proposed methods of estimation as special cases. We also give a general formula for the variance of theT-year eventX
T obtained by the GMM along with a general formula for the parameter estimates and also for the covariances and correlation coefficients between any pair of such estimates. By applying the GMM and carefully choosing the order of the moments that are used in the estimation one can significantly reduce the variance ofT-year events for the range of return periods that are of interest. 相似文献
10.
A modification of the well known Gutenberg-Richter formula leads to the relation $$N(M) = - A_1 + A_2 exp ( - A_3 M)$$ whereN(M) is the cumulative exceedence frequency of an event of magnitudeM. Therefore, from the above generalized formula is concluded that the log cumulative frequency-magnitude relation is not linear. This conclusion is valid for the ranges of magnitudes in contradiction with the classical Gutenberg-Richter relationship. The proposed distribution is bounded to the right. The upper bound is probably related to the maximum magnitude of a certain region or to the maximum magnitude of a given earthquake sample. The values of the upper bound, estimated for numerous samples, are in good agreement with the corresponding values estimated using the third type asymptotic distribution of Gumbel's extreme value statistics. The modified formula of the cumulative frequency-magnitude relation was tested in numerous samples of seismological data from the major area of Greece. The modified relation fits very well at low and high magnitudes range from all earthquake samples where it has been tested. 相似文献
11.
Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory 总被引：1，自引：0，他引：1
V. F. Pisarenko A. Sornette D. Sornette M. V. Rodkin 《Pure and Applied Geophysics》2014,171(8):1599-1624
The present work is a continuation and improvement of the method suggested in Pisarenko et al. (Pure Appl Geophys 165:1–42, 2008) for the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation is to combine the two main limit theorems of Extreme Value Theory (EVT) that allow us to derive the distribution of T-maxima (maximum magnitude occurring in sequential time intervals of duration T) for arbitrary T. This distribution enables one to derive any desired statistical characteristic of the future T-maximum. We propose a method for the estimation of the unknown parameters involved in the two limit theorems corresponding to the Generalized Extreme Value distribution (GEV) and to the Generalized Pareto Distribution (GPD). We establish the direct relations between the parameters of these distributions, which permit to evaluate the distribution of the T-maxima for arbitrary T. The duality between the GEV and GPD provides a new way to check the consistency of the estimation of the tail characteristics of the distribution of earthquake magnitudes for earthquake occurring over an arbitrary time interval. We develop several procedures and check points to decrease the scatter of the estimates and to verify their consistency. We test our full procedure on the global Harvard catalog (1977–2006) and on the Fennoscandia catalog (1900–2005). For the global catalog, we obtain the following estimates: \( \hat{M}_{{\rm max} } \) = 9.53 ± 0.52 and \( \hat{Q}_{10} (0.97) \) = 9.21 ± 0.20. For Fennoscandia, we obtain \( \hat{M}_{{\rm max} } \) = 5.76 ± 0.165 and \( \hat{Q}_{10} (0.97) \) = 5.44 ± 0.073. The estimates of all related parameters for the GEV and GPD, including the most important form parameter, are also provided. We demonstrate again the absence of robustness of the generally accepted parameter characterizing the tail of the magnitude-frequency law, the maximum possible magnitude M max, and study the more stable parameter Q T (q), defined as the q-quantile of the distribution of T-maxima on a future interval of duration T. 相似文献
12.
Summary
A solution of the direct gravity problem for a finite body with variable density is given. The method is based on Green's formula and is applicable when a particular solution of Poisson's equation is known. The attraction due to the body is expressed by integrals over its surface
The exact solution of the direct gravity problem, as known from the theory of two-dimensional fields [1–3], is closely connected with the problem of the analytic continuation of the exterior field of the attracting mass system into its interior. In the first place, this is a problem of determining the singularities of the exterior field, their distribution within the system and their nature. This approach to the solution of the direct problem is also meaningful from the point of view of determining the characteristics of the attracting system and, therefore, also of solving the inverse problem. In the case of two-dimensional fields the methods of analytical continuation were widely developed in a series of well-known papers by V. N. Strakhov, and they are mainly based on the methods of the theory of the functions of the complex variable. These methods were also successfully applied by Tsirulskii and Golizdra [1, 2] in treating the homogeneous and inhomogeneous, two-dimensional direct problem by means of Cauchy's integrals. However, as regards three-dimensional fields a number of fundamental problems has not been solved in this respect.Dedicated to 90th Birthday of Professor Frantiek Fiala 相似文献
13.
W. G. Strupczewski K. Kochanek S. Weglarczyk V. P. Singh 《Stochastic Environmental Research and Risk Assessment (SERRA)》2005,19(4):280-291
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
14.
T.C. Sharma 《水文科学杂志》2017,62(5):760-773
Methods based on the recursive probability, the extreme number theorem, and Markov chain (MC) concepts were applied to predict drought lengths (duration) on the standardized (termed as standardized hydrological index, SHI) sequences of monthly and annual river flows from Atlantic Canada. Results of the study indicated that the MC-based method is the most efficient, reliable and versatile method for predicting drought durations followed by the extreme-number-based method. The recursive-probability-based method was found to be computationally intensive and less efficient, although it provided a powerful means for calibrating the empirical plotting position formula needed in the MC-based method. The Weibull plotting position formula turned out to be a suitable measure of the exceedance probability in MC methodology for predicting drought lengths in Atlantic Canada. Based on results, it can be inferred that the MC-based method can be extended to MC2 and higher-order chains for predicting drought lengths on SHI sequences. The predictive capability of the extreme-number-theorem-based method is limited only to independent or weakly first-order persistent SHI sequences.
EDITOR D. KoutsoyiannisASSOCIATE EDITOR Q. Zhang 相似文献
15.
Philyong Yoon Tae-Woong Kim Chulsang Yoo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1143-1153
Extreme rainfalls in South Korea result mainly from convective storms and typhoon storms during the summer. A proper way for dealing with the extreme rainfalls in hydrologic design is to consider the statistical characteristics of the annual maximum rainfall from two different storms when determining design rainfalls. Therefore, this study introduced a mixed generalized extreme value (GEV) distribution to estimate the rainfall quantile for 57 gauge stations across South Korea and compared the rainfall quantiles with those from conventional rainfall frequency analysis using a single GEV distribution. Overall, these results show that the mixed GEV distribution allows probability behavior to be taken into account during rainfall frequency analysis through the process of parameter estimation. The resulting rainfall quantile estimates were found to be significantly smaller than those determined using a single GEV distribution. The difference of rainfall quantiles was found to be closely correlated with the occurrence probability of typhoon and the distribution parameters. 相似文献
16.
Summary A three-dimensional numerical model of the divided-bar thermal conductivity measuring device that can include both solid and fluid sample portions has been developed. The model has been employed to investigate the effects of porosity in divided-bar measurements and the effects of the distribution of solid sample and contained fluids in porous material on the thermal conductivity calculated from the bar temperature measurements. The results show that the positions of the temperature sensors and thus the nature of the vertical column between the temperature measuring points is of prime importance, and that the sizes of the solid and fluid portions of the sample affect the sample conductivity estimates. The divided bar measures the thermal conductivity parallel to the axis of the bar. Thermal conductivity variations in the radial direction have little effect on the calculated conductivity. Whether or not the sides of the bar are insulated strongly affects the calculated conductivity.Presented at the International Meeting on Terrestrial Heat Flow and the Structure of Lithosphere, Bechyn Castle, Czech Republic, September 2 – 7, 1991. 相似文献
17.
A nonstationary extreme value distribution for analysing the cessation of karst spring discharge 下载免费PDF全文
下载免费PDF全文 Yan Liu Yonghong Hao Yonghui Fan Tongke Wang Xueli Huo Youcun Liu Tian‐Chyi J. Yeh 《水文研究》2014,28(20):5251-5258
The effects of climate change and population growth in recent decades are leading us to consider their combined and potentially extreme consequences, particularly regarding hydrological processes, which can be modeled using a generalized extreme value (GEV) distribution. Most of the GEV models were based on a stationary assumption for hydrological processes, in contrast to the nonstationary reality due to climate change and human activities. In this paper, we present the nonstationary generalized extreme value (NSGEV) distribution and use it to investigate the risk of Niangziguan Springs discharge decreasing to zero. Rather than assuming the location, scale, and shape parameters to be constant as one might do for a stationary GEV distribution analysis, the NSGEV approach can reflect the dynamic processes by defining the GEV parameters as functions of time. Because most of the GEV model is designed to evaluate maxima (e.g. flooding, represented by positive numbers), and spring discharge cessation is a ?minima’, we deduced an NSGEV model for minima by applying opposite numbers, i.e. negative instead of positive numbers. The results of the model application to Niangziguan Springs showed that the probability of zero discharge at Niangziguan Springs will be 1/80 in 2025, and 1/10 in 2030. After 2025, the rate of decrease in spring discharge will accelerate, and the probability that Niangziguan Springs will cease flowing will dramatically increase. The NSGEV model is a robust method for analysing karst spring discharge. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
P. L. Swanson L. H. Estey F. M. Boler S. Billington 《Pure and Applied Geophysics》1992,139(3-4):375-404
The accuracy and precision of microseismic event locations were measured, analyzed, and compared for two types of location systems: anolog and digital. In the first system, relative times of first arrival were estimated from analog signals using automated hardware circuitry; station positions were estimated from mine map coordinates; and event locations were determined using the BLD (Blake, Leighton, and Duvall) direct solution method. In the second system, arrival times were manually measured during interactive displays of digital waveforms; station coordinates were surveyed; and the SW-GBM (Salamon and Wiebols; Godson, Bridges, and McKavanagh) direct basis function was used to solve for locations. Both systems assume constant isotropic seismic velocity of slightly different signals data sets, calibration blast signals with known source site and origin time, and microseismic event signals, were recorded by each location system employing the same array of high-frequency (5 kHz) accelerometers with 150 m maximum dimension. The calibration blast tests indicated a location precision of ±2 m and accuracy of ±10 m for the analog system. Location precision and accuracy for the digital system measured ±1 m and ±8 m, respectively. Numerical experiments were used to assess the contributions of errors in velocity, arrival times, and station positions on the location accuracy and precision for each system. Measured and estimated errors appropriate to each system for microseismic events were simulated in computing source locations for comparison with exact synthetic event locations. Discrepancy vectors between exact locations and locations calculated with known data errors averaged 7.7 and 1.4 m for the analog and digital systems, respectively. These averages are probably more representative of the location precision of microseismic events, since the calibration blast tests produce impulsive seismic arrivals resulting in smaller arrival-time pick errors in the analog system. For both systems, location accuracy is limited by inadequate modeling of the velocity structure. Consequently, when isotropic velocity models are used in the travel-time inversions, the increased effort expended with the digital location system does not, for the particular systems studied, result in increased accuracy. 相似文献
19.
Summary The basic concept of synoptic statistical methods for construction of prognostic charts was outlined by the author in a previous paper. As a result of these investigations it was found that a high correlation exists between time and space means of contourheights of an isobaric surface (850 mb surface). As it has been shown later byPichler this result may be interpreted by assuming that the geopotential fields obeys a numerical solution of the second order homogenous differential equation for wave propagation (hyperbolic equation) provided the phase velocity is given by
. SinceReuter has used for s=666 km and for t=24 hours the conclusion may be drawn that the phase velocity of the wave propagation has an order of magnitude of 5 m/sec. Actually for long waves in the westerlies such a value can be found on an average. The same method can be used for extended forecast procedures if the wave equation is set down for 5 days mean values. Theoretical considerations lead then to a prognostic formula for a 5 days mean chart (8a). This formula can be applied for a sufficient number of grid points in order to construct prognostic charts. The underlying assumption, namely that the mean geopotential field satisfies also a solution of the wave equation turns out to be quite accurate even if only average values of the phase velocity were used for the computation. The usefullness of the method is illustrated for two cases.
Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961). 相似文献
Vortrag gehalten am 7. April 1961 auf der 9. Allgemeinversammlung der «Società Italiana di Geofisica e Meteorologia» (Genova, 6.8. April 1961). 相似文献
20.
The presented approximate formulas yield a critical value of anisotropy parameter , for which an incipient off-axis SV-wave triplication occurs in transversely isotropic media. The formulas are simple but approximate the exact solution with a high accuracy. The best results are obtained using the third-order approximation, which yields accuracy at least 30 times higher than the formulas presented by Thomsen and Dellinger (2003). The formula works safely for parameters = a
33/a
44 > 2 and 0.2 > = (a
11 – a
33)/2a
33 > –0.2, and yields critical values of from 0.1 to 0.7. Outside this interval, it is recommended to use an exact solution. 相似文献