Development of unbiased plotting position formula for General Extreme Value distributions

Goel, N. K.; De, Mallika

doi:10.1007/bf01581563

Cited by 14 publications

(17 citation statements)

References 7 publications

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“…Gringorten ( (Arnell et al, 1986) In-na and P i ¼ nÀiþ0:05cþ0:65 nÀ0:08cþ0:38 À3:8 6 c 6 3:54 Goel and De (1993) P i ¼ iÀ0:02cÀ0:32 nÀ0:04cþ0:36…”

Section: Source Equation Remarkmentioning

confidence: 98%

“…The first and second types have coefficients of skewness in only the numerator and denominator, respectively. The third type is a general form containing a coefficient of skewness in both the denominator and numerator and has been used to derive the plotting position formula in many studies (Arnell et al, 1986;In-na and Nguyen, 1989;Goel and De, 1993). The rest of the formulas have both the squared terms of skewness and coefficient of skewness in both the denominator and numerator.…”

Section: Development Of a Plotting Position Formula For The Gev Distrmentioning

confidence: 98%

“…The existing plotting formulas used in this study were those developed by Gringorten (1963), Cunnane (1978), Arnell et al (1986), In-na and, and Goel and De (1993); they are given in Table 6. The parameter values of Arnell et al (1986) are provided as a table for each shape parameter between À0.3 and +0.1 and for each sample size from 5 to 100.…”

Section: Comparison Between the Derived Formula And Existing Formulasmentioning

confidence: 99%

“…However, In-na and 's formula is difficult to apply to frequency analysis of hydrologic data because the equation was derived from a descending order value. Goel and De (1993) found that the plotting position formula contains a coefficient of skewness for the GEV distribution based on PWM. Haktanir and Bozduman (1995) noted that the appropriate theoretical background for deriving the plotting position for the GEV and log-Pearson type III distributions is a combination of the traditional method and the concept of PWM.…”

Section: Introductionmentioning

confidence: 99%

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Development of plotting position for the general extreme value distribution

Kim

Shin

Joo

et al. 2012

Journal of Hydrology

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“…Gringorten ( (Arnell et al, 1986) In-na and P i ¼ nÀiþ0:05cþ0:65 nÀ0:08cþ0:38 À3:8 6 c 6 3:54 Goel and De (1993) P i ¼ iÀ0:02cÀ0:32 nÀ0:04cþ0:36…”

Section: Source Equation Remarkmentioning

confidence: 98%

Section: Development Of a Plotting Position Formula For The Gev Distrmentioning

confidence: 98%

Section: Comparison Between the Derived Formula And Existing Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Development of plotting position for the general extreme value distribution

Kim

Shin

Joo

et al. 2012

Journal of Hydrology

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“…이러한 확률도시위치를 결정하는 도시위치공식은 1914 년에 Hazen이 제안한 이후 꾸준히 연구되어 왔다 (Weibull, 1939;Beard, 1942;Kimball, 1946;Blom, 1958;Gumbel, 1958;Kimball, 1960;Gringorten, 1963;Filliben, 1969;Benson, 1975;Cunnane, 1978;Adamowski, 1981;Xuewu et al, 1984;Arnell et al, 1986;Nguyen et al, 1989;Guo, 1990b;Nguyen and In-na, 1992;Goel and De, 1993;Haktanir and Bozduman, 1995;De, 2000;김수영 등, 2009). Kimball(1946)은 표본자료의 순서통계량(order statistics) 에 대한 기대값 형태로 나타나는 평균 개념을 적용한 도 시위치를 제안하였으며, Blom(1958) 은 Kimball (1946)이 제안한 개념을 보다 범용적으로 적용할 수 있는       의 관계를 제안한 바 있다.…”

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Derivation of Plotting Position Formulas Considering the Coefficients of Skewness for the GEV Distribution

Kim¹,

Heo²,

Choi³

2011

Journal of Korea Water Resources Association

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Probability plotting position is generally used for the graphical analysis of the annual maximum quantile and the estimation of exceedance probability to display the fitness between sample and an appropriate probability distribution. In addition, it is used to apply a specific goodness of fit test. Plotting position formula to define the probability plotting position has been studied in many researches. Especially, the GEV distribution which is an important probability distribution to analyze the frequency of hydrologic data was popular. In this study, the theoretical reduced variates are derived using the mean value of order statistics to derived an appropriate plotting position formula for the GEV distribution. In addition, various forms of plotting position formula considering various sample sizes and coefficients of skewness related with shape parameters are applied. The parameters of plotting position formulas are estimated using the genetic algorithm. The accuracy of derived plotting position formula is estimated by the errors between the theoretical reduced variates and those by various plotting position formulas including the derived ones in this study. As a result, the errors by derived plotting position formula is the smallest at the range of shape parameter with -0.25～0.10.

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Frequency analysis for predicting 1% annual maximum water levels along Florida coast, US

Huang

2008

Hydrological Processes

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Abstract:In the Coastal Flood Insurance Study by the Federal Emergency Management Agency (FEMA, 2005), 1% annual maximum coastal water levels are used in coastal flood hazard mitigation and engineering design in coastal areas of USA. In this study, a frequency analysis method has been developed to provide more accurate predictions of 1% annual maximum water levels for the Florida coast waters. Using 82 and 94 years of annual maximum water level data at Pensacola and Fernandina, performances of traditional frequency analysis methods, including advanced method of Generalized Extreme Value distribution method, have been evaluated. Comparison with observations of annual maximum water levels with 83 and 95 years of return periods indicate that traditional methods are unable to provide satisfactory predictions of 1% annual maximum water levels to account for hurricane-induced extreme water levels. Based on the characteristics of annual maximum water level distribution of Pensacola and Fernandina stations, a new probability distribution method has been developed in this study. Comparison with observations indicates that the method presented in this study significantly improves the accuracy of predictions of 1% annual maximum water levels. For Fernandina station, predictions of extreme water level match well with the general trend of observations. With a correlation coefficient of 0Ð98, the error for the maximum observed extreme water level of 3Ð11 m (National Geodetic Vertical Datum) with 95 years of return period is 0Ð92%. For Pensacola station, the prediction error for the maximum observed extreme water level with a return period of 83 years is 5Ð5%, with a correlation value of 0Ð98. The frequency analysis has also been reasonably compared to the more costly Monte Carlo simulation method.

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Development of unbiased plotting position formula for General Extreme Value distributions

Cited by 14 publications

References 7 publications

Development of plotting position for the general extreme value distribution

Development of plotting position for the general extreme value distribution

Derivation of Plotting Position Formulas Considering the Coefficients of Skewness for the GEV Distribution

Frequency analysis for predicting 1% annual maximum water levels along Florida coast, US

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