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1.
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
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AbstractFlood 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
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《水文科学杂志》2013,58(4)
Abstract Abstract A complete regional analysis of daily precipitations is carried out in the southern half of the province of Quebec, Canada. The first step of the regional estimation procedure consists of delineating the homogeneous regions within the area of study and testing for homogeneity within each region. The delineation of homogeneous regions is based on using L-moment ratios. A simulation-based testing of statistical homogeneity allows one to verify the inter-site variability. The second step of the procedure deals with the identification of the regional distribution and the estimation of its parameters. The General Extreme Value (GEV) distribution was identified as an appropriate parent distribution. This distribution has already been recommended by several previous research studies for regional frequency analysis of precipitation extremes. The parameters of the GEV distribution are estimated based on the computation of the regional L-CV, L-CS and the mean of annual maximal daily precipitations. The third step consists of the estimation of precipitation quantiles corresponding to various return periods. The final procedure allows for the estimation of these quantiles at sites where no precipitation information is available. The use of a jack-knife resampling procedure with data from the province of Quebec allows one to demonstrate the robustness and efficiency of the regional estimation procedure. Values of the root mean square error were below 10% for a return period of 20 years, and 20% for a return period of 100 years. 相似文献
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Zengchao Hao Vijay P. Singh 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(8):1113-1122
Two entropy-based methods, called ordinary entropy (ENT) method and parameter space expansion method (PSEM), both based on
the principle of maximum entropy, are applied for estimating parameters of the extended Burr XII distribution. With the parameters
so estimated, the Burr XII distribution is applied to six peak flow datasets and quantiles (discharges) corresponding to different
return periods are computed. These two entropy methods are compared with the methods of moments (MOM), probability weighted
moments (PWM) and maximum likelihood estimation (MLE). It is shown that PSEM yields the same quantiles as does MLE for discrete
cases, while ENT is found comparable to the MOM and PWM. For shorter return periods (<10–30 years), quantiles (discharges)
estimated by these four methods are in close agreement, but the differences amongst them grow as the return period increases.
The error in quantiles computed using the four methods becomes larger for return periods greater than 10–30 years. 相似文献
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Hongjoon Shin Taesoon Kim Sooyoung Kim Jun-Haeng Heo 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(2):183-197
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
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Computer-intensive methods are used to examine the fit of the log logistic distribution to annual maxima of Irish rainfall. The characteristics of the L-moment solutions are examined by using the conventional bootstrap on the data and by random sampling within the ellipse of concentration of the parameter estimates. A statistical method of examining uncertainty is provided by the maximum product of spacings solution. Factors derived from random division of an interval are proposed for estimation of short-duration falls for which no data are available. 相似文献
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Parameter and quantile estimation of the 2-parameter kappa distribution by maximum likelihood 总被引：1，自引：1，他引：0
Fran?ois Aucoin Fahim Ashkar Lampouguin Bayentin 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(8):1025-1039
Asymptotic properties of maximum likelihood parameter and quantile estimators of the 2-parameter kappa distribution are studied. Eight methods for obtaining large sample confidence intervals for the shape parameter and for quantiles of this distribution are proposed and compared by using Monte Carlo simulation. The best method is highlighted on the basis of the coverage probability of the confidence intervals that it produces for sample sizes commonly found in practice. For such sample sizes, confidence intervals for quantiles and for the shape parameter are shown to be more accurate if the quantile estimators are assumed to be log normally distributed rather than normally distributed (same for the shape parameter estimator). Also, confidence intervals based on the observed Fisher information matrix perform slightly better than those based on the expected value of this matrix. A hydrological example is provided in which the obtained theoretical results are applied. 相似文献
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kappa值是描述地震动傅里叶幅值谱高频段衰减速率的物理量,其是地震动模拟中的一个重要参数。该研究以临河盆地中部地区为研究区域(N:40°—42°;E:106°—108°),选取2009-2019年盆地内4个强震动台站记录到的16次地震(2≤MS≤6)26条强震数据,利用Anderson与Hough提出的经典算法(傅氏谱法),将加速度记录的水平方向的分量kappa(E-W)与kappa(N-S)分别研究。利用kappa值的均值(kappa(Mean))与震中距的拟合,发现其存在较为明显的线性关系,估算出临河盆地中部地区的高频衰减参数kappa0值为0.044～0.050 s。利用线性关系斜率kR,估算临河盆地中部地区180 km范围内的等效品质因子Q值为2 763～3 367。四个台站的kappa值与震中距分布关系与Castro研究意大利翁布里亚盆地kappa值分布关系一致,存在70至100 km内kappa值有慢增长趋势,此结论验证了我们估算的合理性。 相似文献
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The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 3-parameter log-logistic distribution (LLD3). 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). Simulation results showed that POME's performance was superior in predicting quantiles of large recurrence intervals when population skew was greater than or equal to 2.0. In all other cases, POME's performance was comparable to other methods. 相似文献
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V. P. Singh H. Guo F. X. Yu 《Stochastic Environmental Research and Risk Assessment (SERRA)》1993,7(3):163-177
The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 3-parameter log-logistic distribution (LLD3). 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). Simulation results showed that POME's performance was superior in predicting quantiles of large recurrence intervals when population skew was greater than or equal to 2.0. In all other cases, POME's performance was comparable to other methods. 相似文献
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Zhongmin Liang Wenjuan Chang Binquan Li 《Stochastic Environmental Research and Risk Assessment (SERRA)》2012,26(5):721-730
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
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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
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J.-H. Heo J. D. Salas K.-D. Kim 《Stochastic Environmental Research and Risk Assessment (SERRA)》2001,15(4):284-309
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
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Abstract Applicability of log-Gumbel (LG) and log-logistic (LL) probability distributions in hydrological studies is critically examined under real conditions, where the assumed distribution differs from the true one. The set of alternative distributions consists of five two-parameter distributions with zero lower bound, including LG and LL as well as lognormal (LN), linear diffusion analogy (LD) and gamma (Ga) distributions. The log-Gumbel distribution is considered as both a false and a true distribution. The model error of upper quantiles and of the first two moments is analytically derived for three estimation methods: the method of moments (MOM), the linear moments method (LMM) and the maximum likelihood method (MLM). These estimation methods are used as methods of approximation of one distribution by another distribution. As recommended in the first of this two-part series of papers, MLM turns out to be the worst method, if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e. acceptance of LN, LD or Ga as a hypothetical distribution, while the LG or LL distribution is the true one, gives the MLM bias of reasonable magnitude in upper quantiles. Therefore, one should avoid choosing the LG and LL distributions in flood frequency analysis, especially if MLM is to be applied. 相似文献
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A consistent approach to the frequency analysis of hydrologic data in arid and semiarid regions, i.e. the data series containing several zero values (e.g. monthly precipitation in dry seasons, annual peak flow discharges, etc.), requires using discontinuous probability distribution functions. Such an approach has received relatively limited attention. Along the lines of physically based models, the extensions of the Muskingum‐based models to three parameter forms are considered. Using 44 peak flow series from the USGS data bank, the fitting ability of four three‐parameter models was investigated: (1) the Dirac delta combined with Gamma distribution; (2) the Dirac delta combined with two‐parameter generalized Pareto distribution; (3) the Dirac delta combined with two‐parameter Weibull (DWe) distribution; (4) the kinematic diffusion with one additional parameter that controls the probability of the zero event (KD3). The goodness of fit of the models was assessed and compared both by evaluation of discrepancies between the results of both estimation methods (i.e. the method of moments (MOM) and the maximum likelihood method (MLM)) and using the log of likelihood function as a criterion. In most cases, the DWe distribution with MLM‐estimated parameters showed the best fit of all the three‐parameter models. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions 总被引：2，自引：0，他引：2
G. Salvadori 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(1-2):116-140
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