LH-moment estimation of a four parameter kappa distribution with hydrologic applications

Murshed, Md. Sharwar; Seo, Yun Am; Park, Jeong‐Soo

doi:10.1007/s00477-013-0746-6

Cited by 20 publications

(15 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These L-moments and L-ME have been used widely in many research fields including meteorology, civil engineering, and hydrology (for example, Busababodhin et al, 2016;Meshgi and Khalili, 2009;Murshed et al, 2014;Zhu et al, 2013). We used R package 'lmom' developed by Hosking (2015) to calculate the sample L-moments and the L-ME of GEVD.…”

Section: Methods Of L-moments Estimationmentioning

confidence: 99%

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Lee

Shin

Park

2017

CSAM

Self Cite

View full text Add to dashboard Cite

Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

show abstract

Section: Methods Of L-moments Estimationmentioning

confidence: 99%

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Lee

Shin

Park

2017

CSAM

Self Cite

View full text Add to dashboard Cite

show abstract

“…This method has been used by Murshed et al (2014), and Busababodhin et al (2016). The LH-moments for the BPD are given in Murshed et al (2009).…”

Section: L-momentsmentioning

confidence: 99%

Use of beta-P distribution for modeling hydrologic events

Murshed

Seo

Park

et al. 2018

CSAM

Self Cite

View full text Add to dashboard Cite

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than beta-κ, Gumbel, and GEV distributions.

show abstract

“…L-moments) to the fourth level (L4) to estimate the GEV, GLD, and GPD parameters. Murshed et al [23] investigated the effect and feasibility of the method of LH-moments for estimating heavy-tail conditions by fitting K4D. They indicated that the method can be useful in many practical applications where even the method of L-moments fails to give a feasible solution.…”

Section: Introductionmentioning

confidence: 99%

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

et al. 2017

View full text Add to dashboard Cite

The design of fixed and compliant offshore platforms requires the reliable estimation of extreme values with small probabilities of exceedance based on an appropriate probability distribution. The Weibull distribution is commonly utilised for the statistical analysis of wave crests, including near-field wave run-ups. The parameters are estimated empirically from experimental or onsite measurements. In this paper, the data set of wave crests from a Spar model test was statistically analysed by using the method of LH-moments for parameter estimation of the Weibull distribution. The root-mean-square errors (RMSEs) and the error of LH-kurtosis were used to examine the goodness-of-fit. The results for the first four LH-moments, the estimated parameters, and the probability distributions showed that the level of the LH-moments has a significant influence. At higher levels, the estimation results gave a more focused representation of the upper part of the wave crest distributions, which indicates consistency with the intention of the method of LH-moments. The low tail RMSE values of less than 2.5% demonstrated that a Weibull distribution model estimated by using high-level LH-moments can accurately represent the probability distribution of large extreme wave crests for incident waves, wave run-ups, and moon pool waves. Goodness-of-fit test on the basis of comparison of sampling LH-kurtosis and theoretical LH-kurtosis was recommended as a procedure for selecting an optimum level

show abstract

LH-moment estimation of a four parameter kappa distribution with hydrologic applications

Cited by 20 publications

References 24 publications

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution

Use of beta-P distribution for modeling hydrologic events

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

Contact Info

Product

Resources

About