共查询到20条相似文献,搜索用时 31 毫秒
1.
GEORGE A. GRIFFITHS 《水文科学杂志》2013,58(3):231-248
Abstract The exact distribution of the ratio of any magnitude to the sum of all magnitudes in an annual flood series satisfying the usual distribution-free assumptions of independence and identical distribution, and the additional parametric assumption of exponential tail behaviour with truncation, is shown to be a beta distribution of the first kind. A two-parameter linear transformation of the beta distribution completes the derivation and yields a Wakeby distribution which has the number of members in a series as a given parameter. The Wakeby distribution is developed to illustrate how, in principle, some perceived deficiencies in current flood frequency analysis may be met: more complex parametric assumptions should lead to distributions of wider application. In particular, the distribution has a secure theoretical basis and is hydrologically more realistic because it bounds the variate and requires the definition of a temporally finite annual series. Analytical expressions are obtained for estimating the two distribution parameters; the quantite standard error and a plotting rule. An example is given of the application of the distribution to the design flood problem and an annual flood series is modelled. It is further suggested that a suitable design value for the largest flood to be withstood by a protection work is a statistic of the largest flood occurring during its lifetime. For the derived Wakeby distribution this criterion specifies risk and probability of non-exceedance of the design flood once a lifetime is selected. 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.
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
4.
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
5.
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
6.
FRANCIS M. MUTUA 《水文科学杂志》2013,58(3):235-244
Abstract For a long time now, the hydrologist has been faced with the problem of finding which of the many possible probability distribution functions can be used most effectively in flood frequency analyses. This problem has been mainly due to the insufficiency of the conventional goodness-of-fit procedures when used with the typically skewed flood probability distributions. In this study, the Akaike Information Criterion (AIC) goodness-of-fit test is used to identify more objectively the optimum model for flood frequency analysis in Kenya from a class of competing models. The class is comprised of (a) seven three-parameter density functions, namely, log-normal, Pearson, log-Pearson, Fisher-Tippet, log-Fisher-Tippet, Walter Boughton and log-Walter Boughton; and (b) two five-parameter density functions, namely, Wakeby and log-Wakeby. The AIC is also used in this study as a method of testing for the existence of outlier peak-flow values in the peak annual data used. A modified version of the chi-square goodness-of-fit test is also used, but only for the sake of comparison with the AIC. 相似文献
7.
The index flood procedure coupled with the L‐moments method is applied to the annual flood peaks data taken at all stream‐gauging stations in Turkey having at least 15‐year‐long records. First, screening of the data is done based on the discordancy measure (Di) in terms of the L‐moments. Homogeneity of the total geographical area of Turkey is tested using the L‐moments based heterogeneity measure, H, computed on 500 simulations generated using the four parameter Kappa distribution. The L‐moments analysis of the recorded annual flood peaks data at 543 gauged sites indicates that Turkey as a whole is hydrologically heterogeneous, and 45 of 543 gauged sites are discordant which are discarded from further analyses. The catchment areas of these 543 sites vary from 9·9 to 75121 km2 and their mean annual peak floods vary from 1·72 to 3739·5 m3 s?1. The probability distributions used in the analyses, whose parameters are computed by the L‐moments method are the general extreme values (GEV), generalized logistic (GLO), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA), and five‐parameter Wakeby (WAK). Based on the L‐moment ratio diagrams and the |Zdist|‐statistic criteria, the GEV distribution is identified as the robust distribution for the study area (498 gauged sites). Hence, for estimation of flood magnitudes of various return periods in Turkey, a regional flood frequency relationship is developed using the GEV distribution. Next, the quantiles computed at all of 543 gauged sites by the GEV and the Wakeby distributions are compared with the observed values of the same probability based on two criteria, mean absolute relative error and determination coefficient. Results of these comparisons indicate that both distributions of GEV and Wakeby, whose parameters are computed by the L‐moments method, are adequate in predicting quantile estimates. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
8.
Piyapatr Busababodhin Yun Am Seo Jeong-Soo Park Bung-on Kumphon 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(6):1757-1767
This article discusses the method of higher-order L-moment (LH-moment) estimation for the Wakeby distribution (WAD), and describes and formulates details of parameter estimation using LH-moments for WAD. Monte Carlo simulation is performed, to illustrate the performance of the LH-moment method via heavy-tail quantiles (over all quantiles) using WAD. The LH-moment method proves as useful and effective as the L-moment approach in handling data that follow WAD, and it is then applied to annual maximum flood and wave height data. 相似文献
9.
Regression‐based regional flood frequency analysis (RFFA) methods are widely adopted in hydrology. This paper compares two regression‐based RFFA methods using a Bayesian generalized least squares (GLS) modelling framework; the two are quantile regression technique (QRT) and parameter regression technique (PRT). In this study, the QRT focuses on the development of prediction equations for a flood quantile in the range of 2 to 100 years average recurrence intervals (ARI), while the PRT develops prediction equations for the first three moments of the log Pearson Type 3 (LP3) distribution, which are the mean, standard deviation and skew of the logarithms of the annual maximum flows; these regional parameters are then used to fit the LP3 distribution to estimate the desired flood quantiles at a given site. It has been shown that using a method similar to stepwise regression and by employing a number of statistics such as the model error variance, average variance of prediction, Bayesian information criterion and Akaike information criterion, the best set of explanatory variables in the GLS regression can be identified. In this study, a range of statistics and diagnostic plots have been adopted to evaluate the regression models. The method has been applied to 53 catchments in Tasmania, Australia. It has been found that catchment area and design rainfall intensity are the most important explanatory variables in predicting flood quantiles using the QRT. For the PRT, a total of four explanatory variables were adopted for predicting the mean, standard deviation and skew. The developed regression models satisfy the underlying model assumptions quite well; of importance, no outlier sites are detected in the plots of the regression diagnostics of the adopted regression equations. Based on ‘one‐at‐a‐time cross validation’ and a number of evaluation statistics, it has been found that for Tasmania the QRT provides more accurate flood quantile estimates for the higher ARIs while the PRT provides relatively better estimates for the smaller ARIs. The RFFA techniques presented here can easily be adapted to other Australian states and countries to derive more accurate regional flood predictions. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
10.
Kenechukwu Okoli Korbinian Breinl Luigia Brandimarte Anna Botto Elena Volpi Giuliano Di Baldassarre 《水文科学杂志》2013,58(13-14):1913-1926
ABSTRACTThis study compares model averaging and model selection methods to estimate design floods, while accounting for the observation error that is typically associated with annual maximum flow data. Model selection refers to methods where a single distribution function is chosen based on prior knowledge or by means of selection criteria. Model averaging refers to methods where the results of multiple distribution functions are combined. Numerical experiments were carried out by generating synthetic data using the Wakeby distribution function as the parent distribution. For this study, comparisons were made in terms of relative error and root mean square error (RMSE) referring to the 1-in-100 year flood. The experiments show that model averaging and model selection methods lead to similar results, especially when short samples are drawn from a highly asymmetric parent. Also, taking an arithmetic average of all design flood estimates gives estimated variances similar to those obtained with more complex weighted model averaging. 相似文献
11.
Abstract A graphical test is presented to check if recorded annual maximum flood data for a group of gauging stations in a region belong to a common parent distribution (P). The test compares the observed at site L-coefficient of variation (Lcv) with its sampling distribution. The latter is obtained by generating synthetic sequences from an assumed parent distribution (P). A group of sites is deemed to be homogeneous if the observed Lcv, treated as an order statistic, lies within its sampling distribution. The proposed test has been applied to annual maximum flood data from Tanzania to delineate the country into 12 homogeneous regions. 相似文献
12.
《水文科学杂志》2012,57(15):1867-1892
ABSTRACTThe flood peak is the dominating characteristic in nearly all flood-statistical analyses. Contrary to the general assumptions of design flood estimation, the peak is not closely related to other flood characteristics. Differentiation of floods into types provides a more realistic view. Often different parts of the probability distribution function of annual flood peaks are dominated by different flood types, which raises the question how shifts in flood regimes would modify the statistics of annual maxima. To answer this, a distinction into five flood types is proposed; then, temporal changes in flood-type frequencies are investigated. We show that the frequency of floods caused by heavy rain has increased significantly in recent years. A statistical model is developed that simulates peaks for each event type by type-specific peak–volume relationships. In a simulation study, we show how changes in frequency of flood event type lead to changes in the quantiles of annual maximum series. 相似文献
13.
14.
Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia 总被引:1,自引:1,他引:0
Khaled Haddad Ataur Rahman 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(3):415-428
Selection of a flood frequency distribution and associated parameter estimation procedure is an important step in flood frequency
analysis. This is however a difficult task due to problems in selecting the best fit distribution from a large number of candidate
distributions and parameter estimation procedures available in the literature. This paper presents a case study with flood
data from Tasmania in Australia, which examines four model selection criteria: Akaike Information Criterion (AIC), Akaike
Information Criterion—second order variant (AICc), Bayesian Information Criterion (BIC) and a modified Anderson–Darling Criterion (ADC). It has been found from the Monte
Carlo simulation that ADC is more successful in recognizing the parent distribution correctly than the AIC and BIC when the
parent is a three-parameter distribution. On the other hand, AIC and BIC are better in recognizing the parent distribution
correctly when the parent is a two-parameter distribution. From the seven different probability distributions examined for
Tasmania, it has been found that two-parameter distributions are preferable to three-parameter ones for Tasmania, with Log
Normal appears to be the best selection. The paper also evaluates three most widely used parameter estimation procedures for
the Log Normal distribution: method of moments (MOM), method of maximum likelihood (MLE) and Bayesian Markov Chain Monte Carlo
method (BAY). It has been found that the BAY procedure provides better parameter estimates for the Log Normal distribution,
which results in flood quantile estimates with smaller bias and standard error as compared to the MOM and MLE. The findings
from this study would be useful in flood frequency analyses in other Australian states and other countries in particular,
when selecting an appropriate probability distribution from a number of alternatives. 相似文献
15.
This paper presents an approach to estimating the probability distribution of annual discharges Q based on rainfall-runoff modelling using multiple rainfall events. The approach is based on the prior knowledge about the probability distribution of annual maximum daily totals of rainfall P in a natural catchment, random disaggregation of the totals into hourly values, and rainfall-runoff modelling. The presented Multi-Event Simulation of Extreme Flood method (MESEF) combines design event method based on single-rainfall event modelling, and continuous simulation method used for estimating the maximum discharges of a given exceedance probability using rainfall-runoff models. In the paper, the flood quantiles were estimated using the MESEF method, and then compared to the flood quantiles estimated using classical statistical method based on observed data. 相似文献
16.
Hongjoon Shin Younghun Jung Changsam Jeong Jun-Haeng Heo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(1):105-114
An important problem in frequency analysis is the selection of an appropriate probability distribution for a given sample
data. This selection is generally based on goodness-of-fit tests. The goodness-of-fit method is an effective means of examining
how well a sample data agrees with an assumed probability distribution as its population. However, the goodness of fit test
based on empirical distribution functions gives equal weight to differences between empirical and theoretical distribution
functions corresponding to all observations. To overcome this drawback, the modified Anderson–Darling test was suggested by
Ahmad et al. (1988b). In this study, the critical values of the modified Anderson–Darling test statistics are revised using simulation experiments
with extensions of the shape parameters for the GEV and GLO distributions, and a power study is performed to test the performance
of the modified Anderson–Darling test. The results of the power study show that the modified Anderson–Darling test is more
powerful than traditional tests such as the χ2, Kolmogorov–Smirnov, and Cramer von Mises tests. In addition, to compare the results of these goodness-of-fit tests, the
modified Anderson–Darling test is applied to the annual maximum rainfall data in Korea. 相似文献
17.
Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions
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The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
The objective of the study was to compare the relative accuracy of three methodologies of regional flood frequency analysis in areas of limited flood records. Thirty two drainage basins of different characteristics, located mainly in the southwest region of Saudi Arabia, were selected for the study. In the first methodology, region curves were developed and used together with the mean annual flood, estimated from the characteristics of drainage basin, to estimate flood flows at a location in the basin. The second methodology was to fit probability distribution functions to annual maximum rainfall intensity in a drainage basin. The best fitted probability function was used together with common peak flow models to estimate the annual maximum flood flows in the basin. In the third methodology, duration reduction curves were developed and used together with the average flood flow in a basin to estimate the peak flood flows in the basin. The results obtained from each methodology were compared to the flood records of the selected stations using three statistical measures of goodness-of-fit. The first methodology was found best in a case of having short length of record at a drainage basin. The second methodology produced satisfactory results. Thus, it is recommended in areas where data are not sufficient and/or reliable to utilise the first methodology. 相似文献
19.
Real data on wadi flood flows from Saudi Arabia, Yemen, Oman, Kuwait, UAE, Bahrain and Qatar were used to develop methodologies for the prediction of annual maximum flows and average monthly flows in the Arabian Gulf states. For the prediction of annual maximum floods, three methods have been investigated. In the first method, regional curves were developed and used together with the mean annual flood flow, estimated from the characteristics of the drainage basin, to estimate flood flows at a location in the basin. The second method fits data to various probability distribution functions, with a developed methodology introduced to account for floods generated by more than one system of climate, and the best fitted function was used for flood estimates. In the third method, only floods over a threshold, which depends on characteristics of the drainage basin, were considered and modelled. For the prediction of average monthly flows, stochastic simulation approaches of flood frequency analysis were used. Each of the prediction methods was verified by being applied in 40 different drainage basins. Based on the results obtained, recommendations were made on the best method to be applied (at present) by design engineers in the Arabian Gulf states. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
20.
In flood frequency analysis, a suitable probability distribution function is required in order to establish the flood magnitude-return period relationship. Goodness of fit (GOF) techniques are often employed to select a suitable distribution function in this context. But they have been often criticized for their inability to discriminate between statistical distributions for the same application. This paper investigates the potential utility of subsampling, a resampling technique with the aid of a GOF test to select the best distribution for frequency analysis. The performance of the methodology is assessed by applying the methodology to observed and simulated annual maximum (AM) discharge data series. Several AM series of different record lengths are used as case studies to determine the performance. Numerical analyses are carried out to assess the performance in terms of sample size, subsample size and statistical properties inherent in the AM data series. The proposed methodology is also compared with the standard Anderson–Darling (AD) test. It is found that the methodology is suitable for a longer data series. A better performance is obtained when the subsample size is taken around half of the underlying data sample. The methodology has also outperformed the standard AD test in terms of effectively discriminating between distributions. Overall, all results point that the subsampling technique can be a promising tool in discriminating between distributions. 相似文献