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1.
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   

2.
 A comparison of different methods for estimating T-year events is presented, all based on the Extreme Value Type I distribution. Series of annual maximum flood from ten gauging stations at the New Zealand South Island have been used. Different methods of predicting the 100-year event and the connected uncertainty have been applied: At-site estimation and regional index-flood estimation with and without accounting for intersite correlation using either the method of moments or the method of probability weighted moments for parameter estimation. Furthermore, estimation at ungauged sites were considered applying either a log-linear relationship between at-site mean annual flood and catchment characteristics or a direct log-linear relationship between 100-year events and catchment characteristics. Comparison of the results shows that the existence of at-site measurements significantly diminishes the prediction uncertainty and that the presence of intersite correlation tends to increase the uncertainty. A simulation study revealed that in regional index-flood estimation the method of probability weighted moments is preferable to method of moment estimation with regard to bias and RMSE.  相似文献   

3.
The minimum winter temperature series for the United States Gulf Coast for 1799–1988 (190 values) was subjected to Maximum Entropy Spectral Analysis. Significant periodicities in the QBO region (T-2–3 years) and atT=3.7, 4.5, 5.5, 6.5, 7.5, 12.9, 15.5 and 22 years were detected. Some of these were present in the first half only (1799–1893) while others in the latter half only (1894–1988), indicating a transient nature. Also, more than 50% of the variance was random. Many of the significant periodicities are seen in other geophysical parameters. Some may be harmonics of the 11-year sunspot cycle and the 22-year Hale magnetic sunspot cycle.  相似文献   

4.
The problem of fitting a probability distribution, here log-Pearson Type III distribution, to extreme floods is considered from the point of view of two numerical and three non-numerical criteria. The six techniques of fitting considered include classical techniques (maximum likelihood, moments of logarithms of flows) and new methods such as mixed moments and the generalized method of moments developed by two of the co-authors. The latter method consists of fitting the distribution using moments of different order, in particular the SAM method (Sundry Averages Method) uses the moments of order 0 (geometric mean), 1 (arithmetic mean), –1 (harmonic mean) and leads to a smaller variance of the parameters. The criteria used to select the method of parameter estimation are:
–  - the two statistical criteria of mean square error and bias;
–  - the two computational criteria of program availability and ease of use;
–  - the user-related criterion of acceptability.
These criteria are transformed into value functions or fuzzy set membership functions and then three Multiple Criteria Decision Modelling (MCDM) techniques, namely, composite programming, ELECTRE, and MCQA, are applied to rank the estimation techniques.  相似文献   

5.
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   

6.
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   

7.
Numerical simulations of non-ergodic transport of a non-reactive solute plume by steady-state groundwater flow under a uniform mean velocity, , were conducted in a three-dimensional heterogeneous and statistically isotropic aquifer. The hydraulic conductivity, K(x), is modeled as a random field which is assumed to be log-normally distributed with an exponential covariance. Significant efforts are made to reduce the simulation uncertainties. Ensemble averages of the second spatial moments of the plume and the plume centroid variances were simulated with 1600 Monte Carlo (MC) runs for three variances of log K, Y2=0.09, 0.23, and 0.46, and a square source normal to of three dimensionless lengths. It is showed that 1600 MC runs are needed to obtain stabilized results in mildly heterogeneous aquifers of Y20.5 and that large uncertainty may exist in the simulated results if less MC runs are used, especially for the transverse second spatial moments and the plume centroid variance in transverse directions. The simulated longitudinal second spatial moment and the plume centroid variance in longitudinal direction fit well to the first-order theoretical results while the simulated transverse moments are generally larger than the first-order values. The ergodic condition for the second spatial moments is far from reaching in all cases simulated and transport in transverse directions may reach ergodic condition much slower than that in longitudinal direction.  相似文献   

8.
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   

9.
To obtain the temperatureT and volumeV (or pressureP) dependence of the Anderson-Grüneisen parameter T , measurements with high sensitivity are required. We show two examples:P, V, T measurements of NaCl done with the piston cylinder and elasticity measurements of MgO using a resonance method. In both cases, the sensitivity of the measurements leads to results that provide information about T (,T), where V/V 0 andV 0 is the volume at zero pressure. We demonstrate that determination of T leads to understanding of the volume and temperature dependence ofq=( ln / lnV) T over a broadV, T range, where is the Grüneisen ratio.  相似文献   

10.
The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter generalized Pareto (GP2) distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded by POME were comparable or better within certain ranges of sample size and coefficient of variation.  相似文献   

11.
We develop a new method for the statistical estimation of the tail of the distribution of earthquake sizes recorded in the Harvard catalog of seismic moments converted to m W -magnitudes (1977–2004 and 1977–2006). For this, we suggest a new parametric model for the distribution of main-shock magnitudes, which is composed of two branches, the pure Gutenberg-Richter distribution up to an upper magnitude threshold m 1, followed by another branch with a maximum upper magnitude bound M max, which we refer to as the two-branch model. We find that the number of main events in the catalog (N = 3975 for 1977–2004 and N = 4193 for 1977–2006) is insufficient for a direct estimation of the parameters of this model, due to the inherent instability of the estimation problem. This problem is likely to be the same for any other two-branch model. This inherent limitation can be explained by the fact that only a small fraction of the empirical data populates the second branch. We then show that using the set of maximum magnitudes (the set of T-maxima) in windows of duration T days provides a significant improvement, in particular (i) by minimizing the negative impact of time-clustering of foreshock/main shock/aftershock sequences in the estimation of the tail of magnitude distribution, and (ii) by providing via a simulation method reliable estimates of the biases in the Moment estimation procedure (which turns out to be more efficient than the Maximum Likelihood estimation). We propose a method for the determination of the optimal choice of the T value minimizing the mean-squares-error of the estimation of the form parameter of the GEV distribution approximating the sample distribution of T-maxima, which yields T optimal = 500 days. We have estimated the following quantiles of the distribution of T-maxima for the whole period 1977–2006: Q 16%(M max) = 9.3, Q 50%(M max) = 9.7 and Q 84%(M max) = 10.3. Finally, we suggest two more stable statistical characteristics of the tail of the distribution of earthquake magnitudes: The quantile Q T (q) of a high probability level q for the T-maxima, and the probability of exceedance of a high threshold magnitude ρ T (m*)  = P{m k  ≥ m*}. We obtained the following sample estimates for the global Harvard catalog and The comparison between our estimates for the two periods 1977–2004 and 1977–2006, where the latter period included the great Sumatra earthquake 24.12.2004, m W  = 9.0 confirms the instability of the estimation of the parameter M max and the stability of Q T (q) and ρ T (m*) = P{m k  ≥ m*}.  相似文献   

12.
We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/1+. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10–bm and on the increase ~ 10–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions pr(r) and pg(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother  相似文献   

13.
The palaeo-intensities (F a) of the geomagnetic field in Egypt at some ages are determined by archaeomagnetic measurements and found to be:F a=36.2 T at 3100 B.C., Fa=46.8 T at 3000 B.C.,F a=36.5 T at 2780 B.C., 49.0 T at 2500 B.C., 36.4 T at 2200 B.C., 57.5 T at 1990 B.C., 62.1 T atca 1400 B.C., 61.5 T at 1400 B.C., 69.9 T at 600 B.C., 59.3 T at 550 B.C., 79.9 T at 460 B.C., 73.7 T at 450 B.C., 69.7 T at 320 B.C., 56.2 T at A.D. 50, 64.9 T, at A.D. 400, 54.4 T at A.D. 300, 57.5 T at A.D. 700 and 43.0 T at A.D. 1975.The palaeo-inclinations (I a) at some ages are found to be:I a=24.2° at 420 B.C., 44° at A.D. 50, 60.7° at A.D. 703 and 42° at A.D. 1795.The measured values ofF a are affected by the anisotropy of magnetic susceptibility of the samples by 13% to 20% of the expected correct value. The suitable correction of this effect is by multiplyingF by 1/((1+0.2(/90)) andF by 1/((1–0.13 (/90)), whereF andF are the resultant values ofF a if the laboratory field is perpendicular or parallel to the wall of the sample during the Thelliers' experiments, respectively, and is the angle between the direction of natural remnant magnetization of the sample and the direction of the laboratory field.The results of this paper, together with the previous results for Egypt and the neighbourhoods, lead to the production of the secular variation curve of the geomagnetic field in Egypt for the last 5000 years. The intensity of the field shows a periodicity of about 400 years with multiples.  相似文献   

14.
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   

15.
Abstract

Statistical analysis of extreme events is often carried out to predict large return period events. In this paper, the use of partial L-moments (PL-moments) for estimating hydrological extremes from censored data is compared to that of simple L-moments. Expressions of parameter estimation are derived to fit the generalized logistic (GLO) distribution based on the PL-moments approach. Monte Carlo analysis is used to examine the sampling properties of PL-moments in fitting the GLO distribution to both GLO and non-GLO samples. Finally, both PL-moments and L-moments are used to fit the GLO distribution to 37 annual maximum rainfall series of raingauge station Kampung Lui (3118102) in Selangor, Malaysia, and it is found that analysis of censored rainfall samples of PL-moments would improve the estimation of large return period events.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Zakaria, Z.A., Shabri, A. and Ahmad, U.N., 2012. Estimation of the generalized logistic distribution of extreme events using partial L-moments. Hydrological Sciences Journal, 57 (3), 424–432.  相似文献   

16.
The log-Pearson type 3 distribution is widely used in North America and Australia for fitting annual flood series. Four different versions of the method of moments used in fitting this distribution are compared using Monte Carlo simulated samples which reflect some of the characteristics of annual flood series observed at some Canadian rivers. The bias, standard error, root mean square error, and skew, of the parameter estimates, and of estimates of events associated with different probabilities of occurrence are examined. Also examined are the correlation coefficients between probabilities of occurrence are examined. Also examined are the correlation coefficients between the parameter estimates and between the sample moments that are used in each of the four methods of estimation. It is observed that variances, covariances and correlation coefficients calculated using the usual first-order asymptotic approximation might have considerable error and therefore should be used with caution. On the basis of mean square error of events with return period above the range covered by the sample it is observed that a method proposed earlier which uses moments of order 1, 2 and 3 in real space performs better than the other three methods although certain of the other methods follow the recommendation put forward by some investigators that higher order moments (moments of order 3 or more) should be avoided in flood frequency estimation. It is argued in the present study that the use of higher order moments should not be avoided simply because they have high variability because it is not only the variability of the moments which determines the degree of variability of the estimated design flood events but also the correlation that exists between these moments. Some recommendations are given at the end of the study aimed at achieving better efficiency in flood frequency research at a period where more and more distributions and methods of estimation are being proposed.  相似文献   

17.
Summary One of the important atmospheric levels, the mean energetic level (MEL), which in a sense reflects the energetics of the whole atmosphere, is defined. Its fundamental properties are shown. In order to describe the MEL correctly a new vertical coordinate is introduced and discussed. The new coordinate, , is defined as the ratio of height and temperature. The MEL is shown to be a level with constant value of . Some incorrect conclusions concerning the MEL, derived in the past, have been corrected.List of symbols used c p specific heat of air at constant pressure - c v specific heat of air at constant volume - e base of natural logarithms - E total potential energy - f Coriolis parameter - g acceleration of gravity - i specific internal energy - I internal energy - J enthalpy - k unit vector pointing upwards - p pressure - Q diabatic heating rate - R gas constant of the air - t time - T temperature - v horizontal velocity - v (3) three-dimensional velocity - w vertical velocity in thez-system - z height - temperature growth rate (T/z) - Pechala's vertical coordinate (z/T) - generalized vertical velocity in the -system (d/dt) - specific potential energy - potential energy - density of the air - Ruppert function - T(1–)–1 - ( ) S quantity at the sea level - ( )* quantity at the MEL  相似文献   

18.
Extremes of stream flow and precipitation are commonly modeled by heavytailed distributions. While scrutinizing annual flow maxima or the peaks over threshold, the largest sample elements are quite often suspected to be low quality data, outliers or values corresponding to much longer return periods than the observation period. Since the interest is primarily in the estimation of the right tail (in the case of floods or heavy rainfalls), sensitivity of upper quantiles to largest elements of a series constitutes a problem of special concern. This study investigated the sensitivity problem using the log-Gumbel distribution by generating samples of different sizes (n) and different values of the coefficient of variation by Monte Carlo experiments. Parameters of the log-Gumbel distribution were estimated by the probability weighted moments (PWMs) method, method of moments (MOMs) and maximum likelihood method (MLM), both for complete samples and the samples deprived of their largest elements. In the latter case, the distribution censored by the non-exceedance probability threshold, F T , was considered. Using F T instead of the censored threshold T creates possibility of controlling estimator property. The effect of the F T value on the performance of the quantile estimates was then examined. It is shown that right censoring of data need not reduce an accuracy of large quantile estimates if the method of PWMs or MOMs is employed. Moreover allowing bias of estimates one can get the gain in variance and in mean square error of large quantiles even if ML method is used.  相似文献   

19.
Summary Five ofBerlage's eight empirical rules concerning the Southern Oscillation (1957) may be united in one general rule with regard to the different influence of solar activity during 11-year sunspot cycles with annual maximum numberR above or below 85 (Tables 2, 3, 4, 5 and 6). The opposite character of strong and weak 11-year cycles of solar activity is also present in the 7-year period (Tables 7, 8, 9 and 10; Fig. 1). Finally it is shown that a similar contrast obviously exists in the appearance of polar lights (Table 11, Fig. 2 and 3).The results have not been statistically tested. Because of the rather small number of solar periods involved and the complicated character of the relations found, I could not find a satisfactory statistical method to operate with. I may emphasize, however, the converging evidence enlarging considerably the statistical significance of my results.  相似文献   

20.
Compressional and shear-wave velocities (V p andV s ) were measured during the generalized triaxial deformation (i.e. 1 2=2 3) of pyrophyllite. Observed velocity changes could be ascribed to crack development during dilatancy. Velocity changes were very localized with respect to the ultimate failure plane. The orientation and development of the failure plane was continuously observed with laser holography. Velocity reverals, i.e. changes from a decreasing trend to an increasing trend, were documented in a wet sample in bothV p andV s . These changes in bothV p andV p are inconsistent with dialatancy-diffusion models. The reversals were interpreted as a reflection of local stress reorientation caused by a slowly propagating fault.  相似文献   

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