首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 31 毫秒
1.
 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   

2.
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   

3.
Abstract

Flood frequency analysis (FFA) is essential for water resources management. Long flow records improve the precision of estimated quantiles; however, in some cases, sample size in one location is not sufficient to achieve a reliable estimate of the statistical parameters and thus, regional FFA is commonly used to decrease the uncertainty in the prediction. In this paper, the bias of several commonly used parameter estimators, including L-moment, probability weighted moment and maximum likelihood estimation, applied to the general extreme value (GEV) distribution is evaluated using a Monte Carlo simulation. Two bias compensation approaches: compensation based on the shape parameter, and compensation using three GEV parameters, are proposed based on the analysis and the models are then applied to streamflow records in southern Alberta. Compensation efficiency varies among estimators and between compensation approaches. The results overall suggest that compensation of the bias due to the estimator and short sample size would significantly improve the accuracy of the quantile estimation. In addition, at-site FFA is able to provide reliable estimation based on short data, when accounting for the bias in the estimator appropriately.
Editor D. Koutsoyiannis; Associate editor Sheng Yue  相似文献   

4.
A new bivariate pseudo Pareto distribution is proposed, and its distributional characteristics are investigated. The parameters of this distribution are estimated by the moment-, the maximum likelihood- and the Bayesian method. Point estimators of the parameters are presented for different sample sizes. Asymptotic confidence intervals are constructed and the parameter modeling the dependency between two variables is checked. The performance of the different estimation methods is investigated by using the bootstrap method. A Markov Chain Monte Carlo simulation is conducted to estimate the Bayesian posterior distribution for different sample sizes. For illustrative purposes, a real set of drought data is investigated.  相似文献   

5.
The log-Gumbel distribution is one of the extreme value distributions which has been widely used in flood frequency analysis. This distribution has been examined in this paper regarding quantile estimation and confidence intervals of quantiles. Specific estimation algorithms based on the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood (ML) are presented. The applicability of the estimation procedures and comparison among the methods have been illustrated based on an application example considering the flood data of the St. Mary's River.  相似文献   

6.
The specific objective of the paper is to propose a new flood frequency analysis method considering uncertainty of both probability distribution selection (model uncertainty) and uncertainty of parameter estimation (parameter uncertainty). Based on Bayesian theory sampling distribution of quantiles or design floods coupling these two kinds of uncertainties is derived, not only point estimator but also confidence interval of the quantiles can be provided. Markov Chain Monte Carlo is adopted in order to overcome difficulties to compute the integrals in estimating the sampling distribution. As an example, the proposed method is applied for flood frequency analysis at a gauge in Huai River, China. It has been shown that the approach considering only model uncertainty or parameter uncertainty could not fully account for uncertainties in quantile estimations, instead, method coupling these two uncertainties should be employed. Furthermore, the proposed Bayesian-based method provides not only various quantile estimators, but also quantitative assessment on uncertainties of flood frequency analysis.  相似文献   

7.
Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation.  相似文献   

8.
Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation.  相似文献   

9.
Studies have illustrated the performance of at-site and regional flood quantile estimators. For realistic generalized extreme value (GEV) distributions and short records, a simple index-flood quantile estimator performs better than two-parameter (2P) GEV quantile estimators with probability weighted moment (PWM) estimation using a regional shape parameter and at-site mean and L-coefficient of variation (L-CV), and full three-parameter at-site GEV/PWM quantile estimators. However, as regional heterogeneity or record lengths increase, the 2P-estimator quickly dominates. This paper generalizes the index flood procedure by employing regression with physiographic information to refine a normalized T-year flood estimator. A linear empirical Bayes estimator uses the normalized quantile regression estimator to define a prior distribution which is employed with the normalized 2P-quantile estimator. Monte Carlo simulations indicate that this empirical Bayes estimator does essentially as well as or better than the simpler normalized quantile regression estimator at sites with short records, and performs as well as or better than the 2P-estimator at sites with longer records or smaller L-CV.  相似文献   

10.
 Ad hoc techniques for estimating the quantiles of the Generalized Pareto (GP) and the Generalized Extreme Values (GEV) distributions are introduced. The estimators proposed are based on new estimators of the position and the scale parameters recently introduced in the Literature. They provide valuable estimates of the quantiles of interest both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications). In addition, weakly-consistent estimators are introduced, whose calculation does not require the knowledge of any parameter. The procedures are tested on simulated data, and comparisons with other techniques are shown. The research was partially supported by Contract n. ENV4-CT97-0529 within the project “FRAMEWORK” of the European Community – D.G. XII. Grants by “Progetto Giovani Ricercatori” are also acknowledged.  相似文献   

11.
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   

12.
Q. J. Wang 《Journal of Hydrology》1990,120(1-4):103-114
The concept of partial probability weighted moments (PPWM), which can be used to estimate a distribution from censored samples, is introduced. Unbiased estimators of PPWM are derived. An application is made to estimating parameters and quantiles of the generalized extreme value (GEV) distribution from censored samples. Censored samples yield high quantile estimates which are almost as efficient as those obtained from uncensored samples. This could be a very useful technique for dealing with the undesirable effects of low outliers which occur in semiarid and arid zones.  相似文献   

13.
The robustness of large quantile estimates of largest elements in a small sample by the methods of moments (MOM), L‐moments (LMM) and maximum likelihood (MLM) was evaluated and compared. Bias (B) and mean square error (MSE) were used to measure the estimation methods performance. Quantiles were estimated by eight two‐parameter probability distributions with the variation coefficient being the shape parameter. The effect of dropping largest elements of the series on large quantile values was assessed for various variation coefficient (CV)/sample size (n) ‘combinations’ with n = 30 as the basic value. To that end, both the Monte Carlo sampling experiments and an asymptotic approach consisting in distribution truncation were applied. In general, both sampling and asymptotic approaches point to MLM as the most robust method of the three considered, with respect to bias of large quantiles. Comparing the performance of two other methods, the MOM estimates were found to be more robust for small and moderate hydrological samples drawn from distributions with zero lower‐bound than were the LMM estimates. Extending the evaluation to outliers, it was shown that all the above findings remain valid. However, using the MSE variation as a measure of performance, the LMM was found to be the best for most distribution/variation coefficient combinations, whereas MOM was found to be the worst. Moreover, removal of the largest sample element need not result in a loss of estimation efficiency. The gain in accuracy is observed for the heavy‐tailed and log‐normal distributions, being particularly distinctive for LMM. In practice, while dealing with a single sample deprived of its largest element, one should choose the estimation method giving the lowest MSE of large quantiles. For n = 30 and several distribution/variation coefficient combinations, the MLM outperformed the two other methods in this respect and its supremacy grew with sample size, while MOM was usually the worst. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

14.
ABSTRACT

Flood quantile estimation based on partial duration series (peak over threshold, POT) represents a noteworthy alternative to the classical annual maximum approach since it enlarges the available information spectrum. Here the POT approach is discussed with reference to its benefits in increasing the robustness of flood quantile estimations. The classical POT approach is based on a Poisson distribution for the annual number of exceedences, although this can be questionable in some cases. Therefore, the Poisson distribution is compared with two other distributions (binomial and Gumbel-Schelling). The results show that only rarely is there a difference from the Poisson distribution. In the second part we investigate the robustness of flood quantiles derived from different approaches in the sense of their temporal stability against the occurrence of extreme events. Besides the classical approach using annual maxima series (AMS) with the generalized extreme value distribution and different parameter estimation methods, two different applications of POT are tested. Both are based on monthly maxima above a threshold, but one also uses trimmed L-moments (TL-moments). It is shown how quantile estimations based on this “robust” POT approach (rPOT) become more robust than AMS-based methods, even in the case of occasional extraordinary extreme events.
Editor M.C. Acreman Associate editor A. Viglione  相似文献   

15.
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   

16.
Parametric models are commonly used in frequency analysis of extreme hydrological events. To estimate extreme quantiles associated to high return periods, these models are not always appropriate. Therefore, estimators based on extreme value theory (EVT) are proposed in the literature. The Weissman estimator is one of the popular EVT-based semi-parametric estimators of extreme quantiles. In the present paper we propose a new family of EVT-based semi-parametric estimators of extreme quantiles. To built this new family of estimators, the basic idea consists in assigning the weights to the k observations being used. Numerical experiments on simulated data are performed and a case study is presented. Results show that the proposed estimators are smooth, stable, less sensitive, and less biased than Weissman estimator.  相似文献   

17.
The quantile of a probability distribution, known as return period or hydrological design value of a hydrological variable is the value corresponding to fixed non-exceedence probability and is very important notion in hydrology. In hydraulic engineering design and water resources management, confidence interval (CI) estimation for a population quantile is of primary interest and among other applications, is used to assess the pollution level of a contaminant in water, air etc. The accuracy on such estimation directly influences the engineering investments and safety. The two parameter Weibull, Pareto, Lognormal, Inverse Gaussian, Gamma are some commonly used probability models in such applications. In spite of its practical importance, the problem of CI estimation of a quantile of these widely applicable distributions has been less attended in the literature. In this paper, a new method is proposed to obtain a CI for a quantile of any distribution for which [or the probability distribution of any one-to-one function of the underlying random variable (RV)] generalized pivotal quantities (GPQs) exist for its parameters. The proposed method is elucidated by constructing CIs for quantiles of Weibull, Pareto, Lognormal, Extreme value distribution of type-I for minimum, Exponential and Normal distributions for complete as well as type II singly right censored samples. The empirical performance evaluation of the proposed method evinced that the proposed method has exact well concentrated coverage probabilities near the nominal level even for small uncensored samples as small as 5 and for censored samples as long as the proportion of censored observations is up to 0.70. The existing methods for Weibull distribution have poor or dispersed coverage probabilities with respect to the nominal level for complete samples. Applications of the proposed method in ground water monitoring and in the assessment of air pollution are illustrated for practitioners.  相似文献   

18.
《水文科学杂志》2013,58(2):367-386
Abstract

Extremes of streamflow are usually modelled using heavy tailed distributions. While scrutinising annual flow maxima or the peaks over threshold, the largest elements in a sample are often suspected to be low quality data, outliers or values corresponding to much longer return periods than the observation period. In the case of floods, since the interest is focused mainly on the estimation of the right-hand tail of a distribution function, sensitivity of large quantiles to extreme elements of a series becomes the problem of special concern. This study investigated the sensitivity problem using the log-Gumbel distribution by generating samples of different sizes and different values of the coefficient of L-variation by means of Monte Carlo experiments. Parameters of the log-Gumbel distribution were estimated by the probability weighted moments (PWM) method, both for complete samples and the samples deprived of their largest element. In the latter case Hosking's concept of the “A” type PWM with Type II censoring was employed. The largest value was censored above the random threshold T corresponding to the non-exceedence probability F T. The effect of the F T value on the performance of the quantile estimates was then examined. Experimental results show that omission of the largest sample element need not result in a decrease in the accuracy of large quantile estimates obtained from the log-Gumbel model by the PWM method.  相似文献   

19.
The key problem in nonparametric frequency analysis of flood and droughts is the estimation of the bandwidth parameter which defines the degree of smoothing. Most of the proposed bandwidth estimators have been based on the density function rather than the cumulative distribution function or the quantile that are the primary interest in frequency analysis. We propose a new bandwidth estimator derived from properties of quantile estimators. The estimator builds on work by Altman and Léger (1995). The estimator is compared to the well-known method of least squares cross-validation (LSCV) using synthetic data generated from various parametric distributions used in hydrologic frequency analysis. Simulations suggest that our estimator performs at least as well as, and in many cases better than, the method of LSCV. In particular, the use of the proposed plug-in estimator reduces bias in the estimation as compared to LSCV. When applied to data sets containing observations with identical values, typically the result of rounding or truncation, the LSCV and most other techniques generally underestimates the bandwidth. The proposed technique performs very well in such situations.  相似文献   

20.
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   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号