• Wind and Structures
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• v.9 no.3
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• pp.179-191
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• 2006

Parent wind data are often acknowledged to fit a Weibull probability distribution, implying that wind epoch maxima should fall into the domain of attraction of the Gumbel (Type I) extreme value distribution. However, observations of wind epoch maxima are not fitted well by this distribution and a Generalised Extreme Value (GEV) analysis leading to a Type III fit empirically appears to be better. Thus there is an apparent paradox. The reasons why advocates of the GEV approach seem to prefer it are briefly summarised. This paper gives a detailed analysis of the errors involved when the GEV is fitted to epoch maxima of Weibull origin. It is shown that the results in terms of the shape parameter are an artefact of these errors. The errors are unavoidable with the present sample sizes. If proper significance tests are applied, then the null hypothesis of a Type I fit, as predicted by theory, will almost always be retained. The GEV leads to an unacceptable ambiguity in defining design loads. For these reasons, it is concluded that the GEV approach does not seem to be a sensible option.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Wind and Structures
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• v.31 no.5
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• pp.419-430
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• 2020

Weibull distribution is a conspicuous distribution known for its accuracy and its usage for wind energy analysis. The two and three parameter Weibull distributions are adopted in this study to fit wind speed data. The daily mean wind speed data of Ennore, Tamil Nadu, India has been used to validate the procedure. The parameters are estimated using maximum likelihood method, least square method and moment method. Four statistical tests namely Root mean square error, R2 test, Kolmogorov-Smirnov test and Anderson-Darling test are employed to inspect the fitness of Weibull probability density functions. The value of shape factor, scale factor, wind speed and wind power are determined at a height of 100m using extrapolation of numerical equations. Also, the value of capacity factor is calculated mathematically. This study provides a way to evaluate feasible locations for wind energy assessment, which can be used at any windy site throughout the world.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.3
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• pp.45-55
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• 2000

This study was carried out to derive optimal design low flows bythe Weibull-3 and Wakeby distributions for the partial consecutive duration series at seven watersheds along Han. nagdong, Geum Yeongsan and Seomjin river systems. L-coefficient of variation L-skewness and L-kurtosis were calculated by the L-moment ratio respectively. Parameters were estimated by the method of L-Moments with consecutive duration. Design low flows obtained by method of L-Moments using with consecutive duration, Design low flows obtained by method of L-Moments using different methods for plotting positions formulas in the Weibull-3 and Wakeby distributions were compared by the Root Mean Square Errors(RMSE). It has shown that design low flows derived by the method of L-moments using Weivull plotting position formula in Wakeby distribution were much closer to those of the observed data in comparison with those obtained by the methods of L-moments with the different formulas for plotting positions in Weibull-3 distribution from the viewpoint of Root Mean Square Errors.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.531-536
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• 1999

This study was carried out to derive optimal design drought flows by the Weibull-3 and Wakeby distributions for the annual drought flows series at seven watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. L-coefficient of variation , L-skewness and L-kurtosis were calculated by the L-moment ratio respectivley. Parameters were estimated by the Methods o fL-Moments with continuous duration. Design drought flows obtained by Methods of L-Moments using Weibull plotting positions formula in the Weibull-3 and Wakeby distributions were compared by the Relative Mean Errors(RME), Relative Absolute Errors (RAE) and Root Mean Square Errors(RMSE). It has shown that design drought flows by the Wakeby distribution using method of L-moments are much closer to those of the observed data in comparison with those obtained by the Weibull-3 distribution using method of L-moments.

• Advanced Composite Materials
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• v.16 no.3
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• pp.245-258
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• 2007

The single-modal Weibull model has been assessed on Tyranno ZMI Si-Zr-C-O fiber if a set of shape and scale parameters accurately reproduced the effect of the size of the diameter on strength. The tensile data of a single fiber have been divided into two expedient groups as 'small diameter' group and 'large diameter' group in deriving the parameters, which should be consistent if the Weibull model accurately reproduced the size effect. However, the derived Weibull parameters were inconsistent between the two groups. Thereby the authors have concluded that the parameters of the single-modal Weibull model are dependent on the fiber diameter, so that the model is inadequate to reproduce the strength size effect. On the other hand, Weibull parameters were found consistent between the two groups by excluding the data of 'large mirror zone' sample, which was defined as the sample around 10% mirror zone area of the fracture surface. What is more, the exclusion reduced the strength variance more drastically in the 'large diameter' group than in the 'small diameter' group, even though the 'large mirror zone' samples were found identical in the percentage between the two groups. The authors therefore conclude that diameter limitation to the 'small diameter' group level can lead to drastically less distributed strength values than the estimated strength through the Weibull scaling on the present Tyranno ZMI Si-Zr-C-O fiber.

• Journal of Applied Reliability
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• v.1 no.1
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• pp.17-33
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• 2001

The characteristics of Weibull distribution are investigated as a function of shape parameter. The statistical estimation methods of the shape parameter and statistical comparison methods of two or more shape parameters are studied. Assuming Weibull distribution, statistical analysis of bending-strength data of alumina titanium carbide ceramic matrix composites machined two different methods are performed.

• Journal of the Korean Society of Safety
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• v.21 no.1 s.73
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• pp.53-58
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• 2006

This paper has been addressed on the discharge characteristics of the ignition coil by Weibull function. It analyzed discharge number and amount of discharge using Weibull distribution to know the inter-relationship between partial discharge and mileage. We detected the discharge which happens for 10 seconds. The applied voltage increased by 0.5[kV] at discharge inception voltage. We diagnosed failure rate using the shape parameters. As a result, we confirmed that the failure rate was increased, because the shape parameter showed the value of 5 according to increasing mileage degradation. Also, it is considered to increase the degradation of inner insulator of ignition coil. Because failure rate of virgin was increased from 0[%] to 25[%] after degradation, stability analysis of the ignition coil using Weibull analysis is possible.

• Journal of Korea Water Resources Association
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• v.46 no.6
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• pp.643-653
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• 2013

The most important procedure in frequency analysis is to determine the appropriate probability distribution and to estimate quantiles for a given return period. To perform the frequency analysis, the goodness-of-fit tests should be carried out for judging fitness between obtained data from empirical probability distribution and assumed probability distribution. The previous goodness-of-fit could not consider enough extreme events from the recent climate change. In this study, the critical values of the modified Anderson-Darling test statistics were derived for 3-parameter Weibull distribution and power test was performed to evaluate the performance of the suggested test. Finally, this method was applied to 50 sites in South Korea. The result shows that the power of modified Anderson-Darling test has better than other existing goodness-of-fit tests. Thus, modified Anderson-Darling test will be able to act as a reference of goodness-of-fit test for 3-parameter Weibull model.

• Wind and Structures
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• v.21 no.2
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• pp.203-221
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• 2015

Wind speed is the most important parameter in the design and study of wind energy conversion systems. The weibull distribution is commonly used for wind energy analysis as it can represent the wind variations with an acceptable level of accuracy. In this study, the wind data for 11 cities in Iran have been analysed over a period of one year. The Goodness of fit test is used for testing data fit to weibull distribution. The results show that this data fit to weibull function very well. The scale and shape factors are two parameters of the weibull distribution that depend on the area under study. The kinds of numerical methods commonly used for estimating weibull parameters are reviewed. Their performance for the cities under study was compared according to root mean square and wind energy errors. The result of the study reveals the empirical, modified maximum likelihood estimate of wind speed with minimum error. Also, that the moment and modified maximum likelihood are the best methods for estimating the energy production of wind turbines.