• Wind and Structures
• /
• 제28권6호
• /
• pp.369-380
• /
• 2019

Statistical distributions are very useful in describing wind speed characteristics and in predicting wind power potential of a specified region. Although the Weibull distribution is the most popular one in wind energy literature, it does not seem to be able to perfectly fit all the investigated wind speed data in nature. Thus, many studies are still being conducted to find flexible distribution for modelling wind speed data. In this study, we propose a new Odd-Burr Rayleigh distribution for wind speed characterization. The Odd-Burr Rayleigh distribution with two shape parameters is flexible enough to model different shapes of wind speed data and thus it can be an alternative wind speed distribution for the assessment of wind energy potential. Therefore, suitability of the Odd-Burr Rayleigh distribution is investigated on real wind speed data taken from different regions in the South Africa. Numerical results of the conducted analysis confirm that the new Odd-Burr Rayleigh distribution is suitable for modelling most of the considered real wind speed cases and it also can be used for predicting wind power.

• Journal of Information Technology Applications and Management
• /
• 제28권4호
• /
• pp.13-20
• /
• 2021

In this paper, I was applied the life distribution following linear failure rate distribution, Lindley distribution and Burr-Hatke exponential distribution extensively used in the arena of software reliability and were associated the reliability possessions of the software using the nonhomogeneous Poisson process with finite failure. Furthermore, the average value functions of the life distribution are non-increasing form. Case of the linear failure rate distribution (exponential distribution) than other models, the smaller the estimated value estimation error in comparison with the true value. In terms of accuracy, since Burr-Hatke exponential distribution and exponential distribution model in the linear failure rate distribution have small mean square error values, Burr-Hatke exponential distribution and exponential distribution models were stared as the well-organized model. Also, the linear failure rate distribution (exponential distribution) and Burr-Hatke exponential distribution model, which can be viewed as an effectual model in terms of goodness-of-fit because the larger assessed value of the coefficient of determination than other models. Through this study, software workers can use the design of mean square error, mean value function as a elementary recommendation for discovering software failures.

• Journal of Korea Water Resources Association
• /
• 제50권3호
• /
• pp.211-221
• /
• 2017

In statistical hydrology, various extreme distributions such as the generalized extreme value (GEV), generalized logistic (GLO) and Gumbel (GUM) models have been widely used to analyze the extreme events. In the case of rainfall events in South Korea, the GEV and Gumbel distributions are known to be appropriate among various extreme distribution models. However, the proper probability distribution model may be different depending on the type of extreme events, rainfall duration, region, and statistical characteristics of extreme events. In this regard, it is necessary to apply a wide range of statistical properties that can be represented by the distribution model because it has two shape parameters. In this study, the statistical applicability of rainfall data is analyzed using the Burr XII distribution and the dimensionless L-moment ratio for 620 stations in South Korea. For this purpose, L-skewness and L-kurtosis of the Burr XII distribution are derived and L-moment ratio diagram is drawn and then the applicability of 620 stations was analyzed. As a result, it is found that the Burr XII distribution for the stations of the Han River basin in which L-skewness is relatively larger than L-kurtosis is appropriate, It is possibility of replacing the distribution of commonly used Gumbel or GEV distributions. Therefore, the Burr XII model can be replaced as an appropriate probability model in this basin.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• 제11권3호
• /
• pp.514-522
• /
• 2007

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this parer, Goel-Okumoto and Yamada-Ohba-Osaki model was reviewed, proposes the Burr distribution reliability model, which making out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method, model selection based on SSE, AIC statistics and Kolmogorov distance, for the sake of efficient model, was employed. Analysis of failure using real data set for the sake of proposing shape parameter of the Burr distribution was employed. This analysis of failure data compared with the Burr distribution model and the existing model(using arithmetic and Laplace trend tests, bias tests) is presented.

• Journal of the Korean Statistical Society
• /
• 제36권4호
• /
• pp.579-593
• /
• 2007

The distributional properties of Pr(Y

• Journal of the Korean Data and Information Science Society
• /
• 제15권3호
• /
• pp.625-632
• /
• 2004

We consider the empirical Bayes confidence intervals that attain a specified level of EB coverage for the scale parameter in the Burr distribution under type II censoring data. Also, we compare the coverage probabilities and the expected confidence interval lengths for these confidence intervals through simulation study.

• Journal of the Korean Data and Information Science Society
• /
• 제23권4호
• /
• pp.815-823
• /
• 2012

In this paper reliability growth model in which the operating time between successive failure is a continuous random variable is proposed. This model is for Burr type XII distribution with two parameters which is discussed in two versions: the order statistics and non-homogeneous Poisson process. The two software reliability measures are obtained. The performance for two versions of the suggested model is tested on real data set by U-plot and Y-plot using Kolmogorov distance.

• Communications for Statistical Applications and Methods
• /
• 제13권1호
• /
• pp.89-99
• /
• 2006

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

• Proceedings of the Korea Water Resources Association Conference
• /
• 한국수자원학회 2018년도 학술발표회
• /
• pp.335-335
• /
• 2018

최근 이상기후현상으로 지구상의 여러 지역에서 극치 수문 사상의 발생 빈도와 강도가 날로 증가하고 있는 추세이다. 이에 대해 수공구조물의 설계를 위한 극치강우사상의 빈도해석에 있어서 적절한 확률분포모형의 적용은 매우 중요하다. 이에 수문통계분야에서는 generalized extreme value(GEV), generalized logistic(GLO), Gumbel(GUM) 모형과 같은 극치 분포를 이용한 수문통계적 특성에 대한 접근이 주로 이루어지고 있다. 하지만 우리나라 강우 사상의 경우 GEV 분포와 GUM 분포가 비교적 적합한 것으로 알려져 있지만 하나의 형상매개변수를 가지고 있어 분포 모형이 표현할 수 있는 통계적 특성에 한계를 가지고 있다. 기존의 GEV나 GUM분포로는 적절히 재현되지 않는 자료들을 분석하기 위해서 두 개의 형상매개변수를 가지는 분포형에 대한 연구가 진행되고 있다. 이에 본 연구에서는 두 개의 형상매개변수를 가지는 Burr XII 분포형의 우리나라 극한 강우자료에 대한 적용성을 평가하였다. Burr XII 분포형은 gamma나 exponential 분포 모형처럼 양의 확률변수만을 가지고, Cauchy나 Pareto 분포 모형처럼 두꺼운 꼬리(heavy-tailed distribution) 형상을 나타내기 때문에 비교적 큰 확률변수가 빈번히 나타나는 극치사상에도 적합한 것으로 알려져 있다. 이를 위해 Burr XII 분포 모형을 이용하여 우리나라 강우자료에 대해 지점빈도해석 및 지역빈도해석을 수행하고 우리나라 강우자료에 비교적 적합하다고 알려진 분포인 GEV, GLO, GUM 분포형을 통해 산정된 결과와 비교하였다.

• Journal of Korean Society for Quality Management
• /
• 제44권1호
• /
• pp.167-180
• /
• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.