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

• Communications for Statistical Applications and Methods
• /
• v.21 no.2
• /
• pp.147-160
• /
• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.42 no.3
• /
• pp.45-55
• /
• 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
• /
• 1999.10c
• /
• pp.531-536
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.2
• /
• pp.279-285
• /
• 2008

This paper presents some characterizations of the Weibull distribution by the independence of record values. We prove that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. We show that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent. And we establish that $X{\sim}Weibull(1,{\alpha})$, ${\alpha}>0$ if and only if $\frac{X_{U(n+1)}+X_{U(n)}}{X_{U(n+1)}-X_{U(n)}}$ and $X_{U(n+1)}$ for $n{\geq}1$ are independent.

• Journal of The Korean Society of Grassland and Forage Science
• /
• v.11 no.4
• /
• pp.209-214
• /
• 1991

The germination of seeds is developmentally complex process requiring water uptake, which is regulated by both genotypic and environmental factors. The present study was undertaken to determine the difference in germination characteristics, and to compare the ability of the logistic and Weibull functions to describe the cumulative germination curve when two levels of osmotic potential(0, -5 bar) were put to seeds of alfalfa, tall fescue, orchardgrass, and Kentucky bluegrass. The effects of grass type, osmotic potential, and their interaction on the total germination and coefficient of germination velocity were significant(P<0.01). The Weibull equation for predicting percent cumulative germination curve of alfalfa had significantly lower residuals than the logistic equation regardless of osmotic potential(P<0.01), indicating that the Weibull equation was more efficient than the logistic equation to fit the data of the percent cumulative germination of alfalfa. The rate parameter from the logistic equation was decreased under water stress, whereas the scale and shape parameters were increased. There were significant differences in days to 20% germination estimated from the logistic and Weibull equations.

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

• Journal of Korean Society of Forest Science
• /
• v.61 no.1
• /
• pp.1-7
• /
• 1983

In the estimation of diameter distribution in a stand using Weibull distribution function, the calculation method of experimental distribution was presented in previous paper. This study was to estimate the diameter distribution of Korean pine stands by Weibull distribution which represents Gamma function, with mean diameter and mean basal-area diameter of the random sample trees. The results obtained fitted the diameter distribution in experimental stands. Thus, this method appears to be used for the estimation of diameter distribution in a stand as well as for the analysis and prediction of stand construction for the future.

• Nuclear Engineering and Technology
• /
• v.55 no.5
• /
• pp.1924-1934
• /
• 2023

In this study, the probabilistic fatigue life model for Ni-base alloys was developed based on the Weibull distribution using statistical analysis of fatigue data reported in NUREG/CR-6909 and the new fatigue data of Alloy 52M/152 and 82/182. The developed Weibull model can consider right-censored data (i.e., non-failed data) and quantify the improved safety (or reliability) based on the level of failure probability. The overall margin in the current fatigue design limit model (ASME design curve + NUREG/CR-6909 F_en model) is similar to that of the Weibull model with a cumulative failure probability of approximately 2.5%. The margin in the current fatigue design limit model demonstrated inconsistencies for the Ni-base alloy weld data, whereas the Weibull model showed a consistent margin. Therefore, the Weibull model can systematically mitigate the excessive safety margin.

• Journal of Korean Society of Transportation
• /
• v.5 no.2
• /
• pp.73-80
• /
• 1987

Various procedures for evaluation of traffic noise annoyance have been proposed. However, most of the studies of this type are restricted for improving traffic flow. In this paper, a method to predict the road traffic noise is proposed in terms of equivalent continuous A-Weighted sound pressure level (Leq), based on a probability model. First, distribution of the road traffic noise level are investigated. second, the weibull distribution parameters are estimated by using the quantification theory. Finally, a prediction model of the road traffic noise is proposed based on the weibull distribution model The predicted values of the Leq are closely matched the measured data.