Generalized exponential distribution: different method of estimations

Gupta, Rajeev; Kundu, Debasis

doi:10.1080/00949650108812098

Cited by 323 publications

(170 citation statements)

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“…To obtain estimates of the two parameters, we can solve (22) by using some non-linear regression techniques. These estimators are called percentile estimators, which were also applied and introduced by Gupta and Kundu [24].…”

Section: Percentile Estimatorsmentioning

confidence: 99%

On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution

Chen

Zhang

Cui

2017

MCA

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Usually, the parameters of a Weibull distribution are estimated by maximum likelihood estimation. To reduce the biases of the maximum likelihood estimators (MLEs) of two-parameter Weibull distributions, we propose analytic bias-corrected MLEs. Two other common estimators of Weibull distributions, least-squares estimators and percentiles estimators, are also introduced. Based on a comparison of their performances in the simulation study, we strongly recommend the analytic bias-corrected MLEs for the parameters of Weibull distributions, especially when the sample size is small.

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Section: Percentile Estimatorsmentioning

confidence: 99%

On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution

Chen

Zhang

Cui

2017

MCA

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“…As a model for the parameters of the f • function Generalised Exponential (GE) distribution has been chosen (e.g. Gupta and Kundu, 2000). Among the distributions presented in Eqs.…”

Section: Stationary Casementioning

confidence: 99%

Inundation risk for embanked rivers

Strupczewski

Kochanek

Bogdanowicz

et al. 2013

Hydrol. Earth Syst. Sci.

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Abstract. The Flood Frequency Analysis (FFA) concentrates on probability distribution of peak flows of flood hydrographs. However, examination of floods that haunted and devastated the large parts of Poland lead us to revision of the views on the assessment of flood risk of Polish rivers. It turned out that flooding is caused not only by the overflow of the levee crest but also due to the prolonged exposure to high water on levees structure causing dangerous leaks and breaches that threaten their total destruction. This is because the levees are weakened by long-lasting water pressure and as a matter of fact their damage usually occurs after the culmination has passed the affected location. The probability of inundation is the total of probabilities of exceeding embankment crest by flood peak and the probability of washout of levees. Therefore, in addition to the maximum flow one should also consider the duration of high waters in a river channel.In the paper the new two-component model of flood dynamics: "Duration of high waters-Discharge ThresholdProbability of non-exceedance" (DqF), with the methodology of its parameter estimation was proposed as a completion to the classical FFA methods. Such a model can estimate the duration of stages (flows) of an assumed magnitude with a given probability of exceedance. The model combined with the technical evaluation of the probability of levee breaches due to the duration (d) of flow above alarm stage gives the annual probability of inundation caused by the embankment breaking.The results of theoretical investigation were illustrated by a practical example of the model implementation to the series of daily flow of the Vistula River at Szczucin. Regardless of promising results, the method of risk assessment due to prolonged exposure of levees to high water is still in its infancy despite its great cognitive potential and practical importance.

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“…GE 분포는 Gupta와 Kundu (1999)에서 소개되었으며 와이블분 포, 감마분포 등과 같이 수명자료의 분석에 유용하게 이용된다. Gupta와 Kundu (2001aKundu ( , 2001bKundu ( , 2002Kundu ( , 2007, Raqab (2002) Meier (1958), Efron (1967), Meier (1975), Breslow와 Crowley (1974 Table 3.4, 3.5, 3. 9, 13, 13+, 18, 23, 28+, 31, 34, 45+, 48, 161+ 지수분포를 가정하고, 중도절단분포에 식 (2.1)을 가정하면,β1 = 4/7 = 0.571로 추정하여σ1은 식 (2.6)과 동일하게 되며, 이 경우σ1 = 60.429,λ1 = 1/σ1 = 0.0165가 된다.…”

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The influence of the random censorship model on the estimation of the scale parameter of the exponential distribution

Kim¹

2014

Journal of the Korean Data and Information Science Society

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Generalized exponential distribution: different method of estimations

Cited by 323 publications

References 4 publications

On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution

On the Bias of the Maximum Likelihood Estimators of Parameters of the Weibull Distribution

Inundation risk for embanked rivers

The influence of the random censorship model on the estimation of the scale parameter of the exponential distribution

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