• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.169-174
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• 2013

The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.621-632
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• 2012

Recurrent event data can be easily found in longitudinal studies such as clinical trials, reliability fields, and the social sciences; however, there are a few observations that disappear temporarily in sight during the follow-up and then suddenly reappear without notice like the Young Traffic Offenders Program(YTOP) data collected by Farmer et al. (2000). In this article we focused on inference for a cumulative mean function of the recurrent event data with these incomplete observation gaps. Defining a corresponding risk set would be easily accomplished if we know the exact intervals where the observation gaps occur. However, when they are incomplete (if their starting times are known but their terminating times are unknown) we need to estimate a distribution function for the terminating times of the observation gaps. To accomplish this, we treated them as interval-censored and then estimated their distribution using the EM algorithm proposed by Turnbull (1976). We proposed a nonparametric estimator for the cumulative mean function and also a nonparametric test to compare the cumulative mean functions of two groups. Through simulation we investigated the finite-sample performance of the proposed estimator and proposed test. Finally, we applied the proposed methods to YTOP data.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.189-201
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• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.45-58
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• 2017

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1915-1926
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• 1995

The Fatigue characteristics of 8-harness satin woven CFRP composites with a circular hole are experimentally investigated under constant amplitude tension-tension loading. It is found in this study that the fatigue damage accumulation behavior is very random and history-independent, and the fatigue cumulative damage is linearly related with the mean number of cycles to a specified damage state. From these results, it is known that the fatigue characteristics of CFRP composites satisfy the basic assumptions of Markov chain theory and the parameter of Markov chain model can be determined only by mean and variance of fatigue lives. The predicted distribution of the fatigue cumulative damage using Markov chain model shows a good agreement with the test results. For the fatigue life distribution, Markov chain model makes similar accuracy to 2-parameter Weibull distribution function.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.19 no.4
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• pp.447-457
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• 2021

Graphite Isotope Ratio Method (GIRM) can be used to estimate plutonium production in a graphite-moderated reactor. This study presents verification results for the GIRM combined with a 3-D polynomial regression function to estimate cumulative plutonium production in a graphite-moderated reactor. Using the 3-D Monte-Carlo method, verification was done by comparing the cumulative plutonium production with the GIRM. The GIRM can estimate plutonium production for specific sampling points using a function that is based on an isotope ratio of impurity elements. In this study, the ¹⁰B/¹¹B isotope ratio was chosen and calculated for sampling points. Then, 3-D polynomial regression was used to derive a function that represents a whole core cumulative plutonium production map. To verify the accuracy of the GIRM with polynomial regression, the reference value of plutonium production was calculated using a Monte-Carlo code, MCS, up to 4250 days of depletion. Moreover, the amount of plutonium produced in certain axial layers and fuel pins at 1250, 2250, and 3250 days of depletion was obtained and used for additional verification. As a result, the difference in the total cumulative plutonium production based on the MCS and GIRM results was found below 3.1% with regard to the root mean square (RMS) error.

• Fibers and Polymers
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• v.6 no.4
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• pp.332-335
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• 2005

The fibrogram theory is newly derived from the superposition principle of the conventional staple diagram, in which the left-hand ends of the fibers have to share a common starting point in order for the fiber length distribution to be measured, and the right-hand ends of the fibers form points. It is shown that the fibrogram is the staple diagram of the fiber sample having different random starting points, as well as the double cumulative distribution function of the frequency length function in the length biased sample. Also, the various means, viz. the numerical mean length, numerical mean length in median, length biased mean length, and length biased mean length in median, and the various upper half means, viz. the numerical upper half mean length, numerical upper half mean length in median, length biased upper half mean length, and length biased upper half mean length in median, are discussed in relation to the cotton blending process.

• Journal of The Korean Society of Integrative Medicine
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• v.6 no.4
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• pp.1-13
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• 2018

Purpose : The purpose of this study has been performed to find the relationship between seafarers' cumulative fatigue and stress by evaluating autonomic nervous functions and the results of surveys conducted using questionnaires. Methods : The subjects were seafarers working on various ships (home trade ships) of South Korea, who were healthy adults without any diseases, as confirmed through preliminary surveys were recruited through simple random sampling. A device that measures autonomic nervous functions by analyzing heart rate variability, which is also used often in clinical diagnoses and studies at universities, university hospitals, and general hospitals was used to measure the seafarers' cumulative fatigue and stress. Pearson's correlation analyses were also conducted to test the relationship between cumulative fatigue and stress measured by evaluating autonomic nervous functions and the results of surveys conducted with questionnaires. Results : There was no correlation between mean cumulative fatigue measured for each ship type and seafarers position through autonomic nervous functions evaluation and fatigue severity scale (FSS). There also was no correlation between the mean levels of stress measured for each ship type and seafarers position through autonomic nervous functions evaluation and survey scores of Korean occupational stress scale (KOSS). Conclusion : Therefore, in order to prevent man-made accidents in the sea among seafarers working with irregular port entry/departure schedules and under environments involving continued vibration, noises, and shaking, it is necessary to analyzed cumulative fatigue and stress scientifically and objectively, such as through autonomic nervous functions evaluation rather than through surveys.

• The Transactions of the Korea Information Processing Society
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• v.4 no.1
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• pp.177-183
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• 1997

The cumulative function of the noncentral t distribution calculate power in testing equality of means of two normal populations and confidence intervals for the ratio of population mean to standard deviation. In this paper, the evaluation of the cumulative function of noncentral t distribution is applied to the neural network consists of the multi-layer perception structure and learning process has the algorithm of the backpropagation. Numerical comparisons are made between the Fisher's values and the results obtained by neural network theory.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3892-3898
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• 1996

In this study, the prediction of the fatigue life as well as the extimation of the characteristics of fatigue cumulative damage on GFRP under random loading were performed. The constant amplitude tests and the ramdom loading test were carried on notched GFRP specimens with a circular hole. Random waves were generated with a micro-computer and had wide band spectra. Since it is useful that the prediction of fatigue life ot the given load sequences is based on S-N curves under constant amplitude loading, the estimation of equivalent stress is done on every random waves. The equivalent stress wasat first estimated by Miner's rule and then by the proposed model which was based on Hashin-Rotem's comulative damage theory regarding nonlinear fatigue cumulative damage behavior. The fatigue lives were predicted from each equivalent stress evaluated. And each predicted fatigue llife was compared with experimental results. The number of cycles of random loads were counted by mean-cross counting method. The reuslts showed that the fatigue life predicted by proposed model was correlated well with the experimental results in comparison with Miner's model.