• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.259-268
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• 2006

For Type-II censored sample, we propose three modified entropy estimators based on the Vasieck's estimator, van Es' estimator, and Correa's estimator. We also propose the goodness-of-fit tests of the Weibull distribution based on the modified entropy estimators. We simulate the mean squared errors (MSE) of the proposed entropy estimators and the powers of the proposed tests. We also compare the proposed tests with the modified Kolmogorov-Smirnov and Cramer-von-Mises tests which were proposed by Kang et al. (2003).

• Korean Chemical Engineering Research
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• v.46 no.1
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• pp.56-62
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• 2008

Characteristics of heat transfer were investigated in a three-phase swirling fluidized bed whose diameter was 0.102 m and 2.5 m in height. Effects of gas and liquid velocities, particle size and liquid swirling ratio ($R_S$) on the immersed heater-to-bed overall heat transfer coefficient were examined. The heat transfer characteristics between the immersed heater and the bed was well analyzed by means of phase space portraits and Kolmogorov entropy(K) of the time series of temperature difference fluctuations. The phase space portraits of temperature difference fluctuations became stable and periodic and the value of Kolmogorov entropy tended to decrease with increasing the value of liquid swirling ratio from 0.1 to 0.4. The value of Kolmogorov entropy exhibited its minimum with increasing liquid swirling ratio. The value of overall heat transfer coefficient (h) showed its maximum with the variation of liquid velocity, bed porosity or liquid swirling ratio, but it increased with increasing gas velocity and particle size. The value of K exhibited its maximum at the liquid velocity at which the h value attained its maximum. The overall heat transfer coefficient and Kolmogorov entropy were well correlated in terms of dimensionless groups and operating variables.

• Korean Chemical Engineering Research
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• v.47 no.4
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• pp.481-487
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• 2009

In this of study, effects of input air velocity(0.05~0.22 m/sec) and molten carbonate salt temperature ($870{\sim}970^{\circ}C$) on flow regime transition have been studied by adopting a drift-flux model of air holdup and a stochastic analysis of differential pressure fluctuations in an air-molten sodium carbonate salt two-phase system(molten salt oxidation process). Air holdup where the flow regime transition begins was determined by air holdup-drift flux plot. The air holdup value which the flow regime transition begins was increased with increasing molten carbonate salt temperature due to the decrease of viscosity and surface tension of molten carbonate salt. To characterize the flow regime transition more quantitatively, differential pressure fluctuation signals have been analyzed by adopting the stochastic method such as phase space portraits and Kolmogorov entropy, The Kolmogorov entropy decreased with an increasing of molten carbonate salt temperature but increased gradually with an increase in an air velocity, however, it exhibited different tendency with the flow regime and the air velocity value which flow regime transition begins was same to the results of drift-flux analysis.

• Applied Chemistry for Engineering
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• v.17 no.1
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• pp.93-99
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• 2006

Methods to distinguish flow regimes in gas-solid fluidized bed have been investigated by adopting the concept of chaos theory. Pressure fluctuations have been chosen as a state variable for the analysis of the system. Pressure fluctuations obtained from differential pressure transducer have been investigated using the chaos analysis (Correlation dimension and Kolmogorov entropy) as well as the average and standard deviation. As a result, fluidization regimes in gas-solid fluidized bed can be distinguished by statistics methods as the average and standard deviation. Also, Correlation dimension and Kolmogorov entropy could be used to classify the fluidization regimes.

• Korean Chemical Engineering Research
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• v.44 no.5
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• pp.505-512
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• 2006

Characteristics of particle holdup and heat transfer were investigated in a liquid-particle swirling fluidized bed whose diameter was 0.102 m and 2.5 m in height. Effects of liquid velocity, particle size and swirling liquid ratio($R_s$) on the particle holdup and immersed heater-to-bed overall heat transfer coefficient were examined. The particle holdup increased with increasing particle size and swirling liquid ratio but decreased with increasing liquid velocity.The local particle holdup was relatively high in the region near the heater when the $R_s$ value was 0.1~0.3, but the radial particle holdup was almost uniform when the $R_s$ value was 0.5, whereas, when the $R_s$ value was 0.7, the local particle holdup was relatively low in the region near the heater. The heat transfer characteristics between the immersed heater and the bed was well analyzed by means of phase space portraits and Kolmogorov entropy(K) of the time series of temperature difference fluctuations. The phase space portraits of temperature difference fluctuations became stable and periodic and the value of Kolmogorov entropy tended to decrease with increasing the value of $R_s$ from 0.1 to 0.5. The Kolmogorov entropy exhibited its maximum value with increasing liquid velocity. The value of overall heat transfer coefficient(h) showed its maximum value with the variation of liquid velocity, bed porosity or swirling liquid ratio, but it increased with increasing particle size. The value of K exhibited its maximum at the liquid velocity at which the h value attained its maximum. The particle holdup and overall heat transfer coefficient were well correlated in terms of dimensionless groups of operating variables.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.909-918
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• 1999

Arizono and Ohta(1989) studied goodness of fit test of normality using the entropy estimator proposed by Vasicek (1976) Recently van Es(1992) and Correa(1995) proposed an estimator of entropy. In this paper we propose goodness of fit test statistics for normality based on Vasicek ven Es and Correa. And we compare the power of the proposed test statistics with Kolmogorov-Smirnov Kuiper Cramer von Mises Watson Anderson-Darling and Finkelstein and Schefer statistics.

• Journal of Korea Society of Industrial Information Systems
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• v.5 no.2
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• pp.39-46
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• 2000

Recent]y van Es (1992) and Correa (1995) proposed an estimator of entropy. In this paper, we proposed the goodness of fit test statistics for exponentiality based on Vasicek's estimator and Correa's estimator of Kullback-Leibier Information. And we compare the power of the proposed test statistics with Kolmogorov-Sminov, Kuiper, Cramer von Mises, Watson, Andersen-Darling and Finkelstein and Schefer statistics.