A review of methods of parameter estimation for the extreme value type-1 distribution

Phien, Huynh Ngoc

doi:10.1016/0022-1694(87)90070-9

Cited by 58 publications

(22 citation statements)

References 14 publications

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“…The variance of the T-year event estimator due to sampling uncertainty in this case is given by Phien (1987) as Varfx x T g ¼ a 2 n À 1 1:11 À 0:907 n þ 0:457 À 1:17 n y T þ 0:805 À 0:186 n y 2 T ! ð9Þ…”

Section: Methods Of Probability Weighted Momentsmentioning

confidence: 99%

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Comparison of regional index flood estimation procedures based on the extreme value type I distribution

Kjeldsen

Rosbjerg²

2002

Stochastic Environmental Research and Risk Assessment (SERRA)

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A comparison of different methods for estimating T-year events is presented, all based on the Extreme Value Type I distribution. Series of annual maximum flood from ten gauging stations at the New Zealand South Island have been used. Different methods of predicting the 100-year event and the connected uncertainty have been applied: At-site estimation and regional index-flood estimation with and without accounting for intersite correlation using either the method of moments or the method of probability weighted moments for parameter estimation. Furthermore, estimation at ungauged sites were considered applying either a log-linear relationship between at-site mean annual flood and catchment characteristics or a direct log-linear relationship between 100-year events and catchment characteristics. Comparison of the results shows that the existence of at-site measurements significantly diminishes the prediction uncertainty and that the presence of intersite correlation tends to increase the uncertainty. A simulation study revealed that in regional index-flood estimation the method of probability weighted moments is preferable to method of moment estimation with regard to bias and RMSE.

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Section: Methods Of Probability Weighted Momentsmentioning

confidence: 99%

“…The extreme value type I (EV-I) distribution is commonly used for estimation of extreme hydrological events, see for example Jain and Singh (1987) and Phien (1987). At-site estimation of extreme events is often hampered by lack of information leading to increased prediction uncertainty in the estimation of Tyear events.…”

Section: Introductionmentioning

confidence: 99%

Comparison of regional index flood estimation procedures based on the extreme value type I distribution

Kjeldsen

Rosbjerg²

2002

Stochastic Environmental Research and Risk Assessment (SERRA)

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“…But, the method has the disadvantage of frequently giving biased estimates and often failed to give the desired accuracy in estimating extremes from hydrological data. It may not produce good estimators in small samples, especially when the random variable is restricted to an interval that depends on the parameters [4][5][6]. PWM and MLS are much less complicated, and the computations are simpler.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Estimators of Gumbel Distribution for Modelling Wind Speed Data

Vivekanandan¹

2012

BIJDM

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“…The regional models developed could be successfully used in predicting flood quantiles needed in hydrological design for ungauged catchments within the region studied and without any available historic flood information. The assumption that the missing annual flood flows at the sites of interest fit the EV1 distribution is considered to be a reasonable approximation justified by the hydrological experience from the region and by the wide applicability of the EV1 distribution in analysing annual extremes (Phien, 1987). The models, as for all regional models, cannot take into account future changes in the catchments and cannot be safely applied outside the region of the study.…”

Section: Prediction Of Flood Quantiles For Ungauged Catchmentsmentioning

confidence: 99%

Predicting the mean annual flood and flood quantiles for ungauged catchments in Greece

Mimikou

Gordios

1989

Hydrological Sciences Journal

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The spatial variation of the mean annual flood of both mean daily and instantaneous extremes and of the parameters of the Extreme Value Type 1 (EV1) distribution for catchments in the northwest and west regions of Greece are significantly explained in terms of physiographic and climatological characteristics of the catchments by using multiple regression techniques. The catchment characteristics used in the study are the following: drainage area, mean annual areal precipitation, stream frequency, main stream slope and length, intensity of the one-day rainfall of five-year return period, and a soil type index. The EV1 distribution has been found to describe adequately the annual frequency distributions of the daily and of the standardised by-their-mean-value daily extremes of the catchments. Based on the regional models for the parameters of the distribution, annual flood frequency curves, and thus flood quantiles of the assumed distribution, can be derived. The developed regional models are successfully used in predicting with satisfactory accuracy the mean annual floods and flood quantiles, needed in hydrological design, for ungauged catchments within the region studied.Les prévision de la crue moyenne annuelle et les quantiles de la crue pour des bassins non-observés en Grèce. Résumé Les variations de la crue moyenne annuelle et des paramètres de la distribution EV1 pour des bassins du NordOuest de la Grèce sont expliquée en fonction des caractéris-tiques géomorphologiques des bassins i.e. aire du bassin, précipitation moyenne annuelle du bassin, la densité de drainage, la pente et longueur du cours principal, l'intensité de la pluie journalière pour une période de retour de cinq ans et l'index du type du sol. Les modèles régionaux résultant de l'étude prédisent avec une précision satisfaisante les crues moyennes annuelles et les quantiles qui sont nécessaires pour les calculs hydrologiques des ingénieurs pour les bassins nonobservés de la région étudiée.

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A review of methods of parameter estimation for the extreme value type-1 distribution

Cited by 58 publications

References 14 publications

Comparison of regional index flood estimation procedures based on the extreme value type I distribution

Comparison of regional index flood estimation procedures based on the extreme value type I distribution

Comparison of Estimators of Gumbel Distribution for Modelling Wind Speed Data

Predicting the mean annual flood and flood quantiles for ungauged catchments in Greece

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