• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Journal of Wind Energy
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• v.14 no.1
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• pp.37-43
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• 2023

In this study, synthetic time series wind data was generated numerically using a second-order Markov chain. One year of wind data in 2020 measured by the AWS on Wido Island was used to investigate the statistics for measured wind data. Both the transition probability matrix and the cumulative transition probability matrix for annual hourly mean wind speed were obtained through statistical analysis. Probability density distribution along the wind speed and autocorrelation according to time were compared with the first- and the second-order Markov chains with various lengths of time series wind data. Probability density distributions for measured wind data and synthetic wind data using the first- and the second-order Markov chains were also compared to each other. For the case of the second-order Markov chain, some improvement of the autocorrelation was verified. It turns out that the autocorrelation converges to zero according to increasing the wind speed when the data size is sufficiently large. The generation of artificial wind data is expected to be useful as input data for virtual digital twin wind turbines.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.797-810
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• 2017

The Korean peninsula is exposed to typhoons every year. Typhoons cause huge socioeconomic damage because tropical cyclones tend to occur with strong winds and heavy precipitation. In order to understand the complex dependence structure between strong winds and heavy precipitation, the copula links a set of univariate distributions to a multivariate distribution and has been actively studied in the field of hydrology. In this study, we carried out analysis using data of wind speed and precipitation collected from the weather stations in Busan and Jeju. Log-Normal, Gamma, and Weibull distributions were considered to explain marginal distributions of the copula. Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling test statistics were employed for testing the goodness-of-fit of marginal distribution. Observed pseudo data were calculated through inverse transformation method for establishing the copula. Elliptical, archimedean, and extreme copula were considered to explain the dependence structure between strong winds and heavy precipitation. In selecting the best copula, we employed the Cramer-von-Mises test and cross-validation. In Busan, precipitation according to average wind speed followed t copula and precipitation just as maximum wind speed adopted Clayton copula. In Jeju, precipitation according to maximum wind speed complied Normal copula and average wind speed as stated in precipitation followed Frank copula and maximum wind speed according to precipitation observed Husler-Reiss copula.

• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.89-104
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• 1995

This paper is concerned with the method of estimating lifetime distributin from field data for products with multiple modes of failure. When product failures occur within warranty period, a manufacturer can obtain failure-record data; failure times, causes of failure, and covariates. Since these data are seriously incomplete for satisfactory inference, that is, only failures occured during warrantly period may be recorded, it is usually necessary to incoporate the failure-record data by taking a supplementary sample of items obtained following up a portion of products that survive warranty time. The log linear function is considered as a model for describing the relation between failure time of a product and covariates. General methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and their asymptotic properties are studied, and specific formulas for exponential or Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extensions to calendar time warranty or calendar and obtaining time warranty are also considered.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.6
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• pp.2893-2900
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• 2014

Background: Statistical methods are very important to precisely measure breast cancer patient survival times for healthcare management. Previous studies considered basic statistics to measure survival times without incorporating statistical modeling strategies. The objective of this study was to develop a data-based statistical probability model from the female breast cancer patients' survival times by using the Bayesian approach to predict future inferences of survival times. Materials and Methods: A random sample of 500 female patients was selected from the Surveillance Epidemiology and End Results cancer registry database. For goodness of fit, the standard model building criteria were used. The Bayesian approach is used to obtain the predictive survival times from the data-based Exponentiated Exponential Model. Markov Chain Monte Carlo method was used to obtain the summary results for predictive inference. Results: The highest number of female breast cancer patients was found in California and the lowest in New Mexico. The majority of them were married. The mean (SD) age at diagnosis (in years) was 60.92 (14.92). The mean (SD) survival time (in months) for female patients was 90.33 (83.10). The Exponentiated Exponential Model found better fits for the female survival times compared to the Exponentiated Weibull Model. The Bayesian method is used to obtain predictive inference for future survival times. Conclusions: The findings with the proposed modeling strategy will assist healthcare researchers and providers to precisely predict future survival estimates as the recent growing challenges of analyzing healthcare data have created new demand for model-based survival estimates. The application of Bayesian will produce precise estimates of future survival times.

• Journal of dental hygiene science
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• v.18 no.1
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• pp.42-49
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• 2018

The computer-aided design/computer-aided manufacturing (CAD/CAM) system was introduced to shorten the production time of all-ceramic restorations and the number of patient visits. Among these types of ceramic for dental CAD/CAM, they have been processed into inlay, onlay, and crown shapes using leucite-reinforced glass-ceramics to improve strength. The purpose of this study was to observe the mechanical properties and microstructure of leucite-reinforced glass-ceramics for dental CAD/CAM. Two types of leucite-reinforced glass-ceramic blocks (IPS Empress CAD, Rosetta BM) were prepared with diameter of 13 mm and thickness of 1 mm. Biaxial flexural testing was conducted using a piston-on-three-ball method at a crosshead speed of 0.5 mm/min. Weibull statistics were used for the analysis of biaxial flexural strength. Fracture toughness was obtained using an indentation fracture method. Specimens were observed by field emission scanning electron microscopy to examine the microstructure of the leucite crystalline phase after acid etching with 0.5% hydrofluoric acid aqueous solution for 1 minute. The results of strength testing showed that IPS Empress CAD had a mean value of $158.1{\pm}8.6MPa$ and Rosetta BM of $172.3{\pm}8.3MPa$. The fracture toughness results showed that IPS Empress CAD had a mean value of $1.28{\pm}0.19MPa{\cdot}m^{1/2}$ and Rosetta BM of $1.38{\pm}0.12MPa{\cdot}m^{1/2}$. The Rosetta BM sample exhibited higher strength and fracture toughness. Moreover, the crystalline phase size and ratio were increased in the Rosetta BM sample. The above results are expected to elucidate the basic mechanical properties and crystal structure characteristics of IPS Empress CAD and Rosetta BM. Additionally, they will help develop leucite-reinforced glass-ceramic materials for CAD/CAM.

• Journal of the Korean Ceramic Society
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• v.52 no.6
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• pp.441-448
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• 2015

Silicon carbide (SiC) coatings for tri-isotropic (TRISO) nuclear fuel particles were fabricated using a chemical vapor deposition (CVD) process onto graphite. A micro-tensile-testing system was developed for the mechanical characterization of SiC coatings at high temperatures. The fracture strength of the SiC coatings was characterized by the developed micro-tensile test in the range of $25^{\circ}C$ to $1000^{\circ}C$. Two types of CVD-SiC films were prepared for the micro-tensile test. SiC-A exhibited a large grain size (0.4 ~ 0.6 m) and the [111] preferred orientation, while SiC-B had a small grain size (0.2 ~ 0.3 mm) and the [220] preferred orientation. Free silicon (Si) was co-deposited onto SiC-B, and stacking faults also existed in the SiC-B structure. The fracture strengths of the CVD-SiC coatings, as measured by the high-temperature micro-tensile test, decreased with the testing temperature. The high-temperature fracture strengths of CVD-SiC coatings were related to the microstructure and defects of the CVD-SiC coatings.

• Convergence Security Journal
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• v.6 no.3
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• pp.117-126
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• 2006

Bayesian inference and model selection method for software reliability growth models are studied. Software reliability growth models are used in testing stages of software development to model the error content and time intervals between software failures. In this paper, could avoid multiple integration using Gibbs sampling, which is a kind of Markov Chain Monte Carlo method to compute the posterior distribution. Bayesian inference for general order statistics models in software reliability with diffuse prior information and model selection method are studied. For model determination and selection, explored goodness of fit (the error sum of squares), trend tests. The methodology developed in this paper is exemplified with a software reliability random data set introduced by of Weibull distribution(shape 2 & scale 5) of Minitab (version 14) statistical package.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.873-882
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• 2010

This paper considers a Bayesian approach to replacement policy following the expiration of non-renewing combination warranty. The non-renewing combination warranty is the combination of the non-renewing free replacement warranty and the non-renewing pro-rata replacement warranty. We use the criterion based on the expected cost and the expected downtime to determine the optimal replacement period. To do so, we obtain the expected cost rate per unit time and the expected downtime per unit time, respectively. When the failure times are assumed to follow a Weibull distribution with uncertain parameters, we propose the optimal replacement policy based on the Bayesian approach. The overall value function suggested by Jiang and Ji (2002) is utilized to determine the optimal replacement period. Also, the numerical examples are presented for illustrative purpose.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.327-336
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• 2014

Recurrent event data occurs when a subject experiences same type of event repeatedly and is found in various areas such as the social sciences, Economics, medicine and public health. To analyze recurrent event data either a total time or a gap time is adopted according to research interest. In this paper, we analyze recurrent event data with incomplete observation gap using a gap time scale. That is, some subjects leave temporarily from a study and return after a while. But it is not available when the observation gaps terminate. We adopt an interval censoring mechanism for estimating the termination time. Furthermore, to model the association among gap times of a subject, a frailty effect is incorporated into a model. Programs included in Survival package of R program are implemented to estimate the covariate effect as well as the variance of frailty effect. YTOP (Young Traffic Offenders Program) data is analyzed with both proportional hazard model and a weibull regression model.