LH-Moments of Some Distributions Useful in Hydrology

Murshed, Md. Sharwar; Park, Byung‐Jun; Jeong, Bo-Yoon; Park, Jeong‐Soo

doi:10.5351/ckss.2009.16.4.647

Cited by 14 publications

(19 citation statements)

References 15 publications

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“…Previous researches have applied it into fitting with hydrological distributions [16][17][18], which have revealed the limitation in the usage of the proposed LH moments. Many studies introduced the LH moments, but there are still rare studies about its corresponding calculation methods.…”

Section: Lh Momentsmentioning

confidence: 99%

See 1 more Smart Citation

Higher moments method for generalized Pareto distribution in flood frequency analysis

Zhou

Chen

Huang

et al. 2017

IOP Conf. Ser.: Earth Environ. Sci.

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Section: Lh Momentsmentioning

confidence: 99%

“…They are linear combinations of PWM and have shown excellent performances as estimators [13][14][15]. PWM are essential components of L-Moments, and PWM ( r  with 2 , 1 , 0  r ) can be calculated by equation (18).…”

Section: L-momentsmentioning

confidence: 99%

Higher moments method for generalized Pareto distribution in flood frequency analysis

Zhou

Chen

Huang

et al. 2017

IOP Conf. Ser.: Earth Environ. Sci.

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“…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

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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.

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“…Murshed et al [35] formulated LH-moments for a few distributions used in hydrology, namely generalized Gumbel distribution, three parameter kappa distributions, beta-p distribution, and beta-k distribution. Deka et al [36] identifi ed GPA distribution as best using LH-moments when the level of LH-moment is zero.…”

Section: Introductionmentioning

confidence: 99%

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

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LH-Moments of Some Distributions Useful in Hydrology

Cited by 14 publications

References 15 publications

Higher moments method for generalized Pareto distribution in flood frequency analysis

Higher moments method for generalized Pareto distribution in flood frequency analysis

Use of beta-P distribution for modeling hydrologic events

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

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