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CONVERGENCE RATES FOR THE MOMENTS OF EXTREMES
Zuoxiang Peng,Saralees Nadarajah 대한수학회 2012 대한수학회보 Vol.49 No.3
Let X1, X2,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.
CONVERGENCE RATES FOR THE MOMENTS OF EXTREMES
Peng, Zuoxiang,Nadarajah, Saralees Korean Mathematical Society 2012 대한수학회보 Vol.49 No.3
Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.
Convergence rate of extremes for the generalized short-tailed symmetric distribution
Fuming Lin,Zuoxiang Peng,Kaizhi Yu 대한수학회 2016 대한수학회보 Vol.53 No.5
Denote $M_{n}$ the maximum of $n$ independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_{n}$ to $\exp(-e^{-x})$ and the supremum-metric-based convergence rate as well.
Fuming Lin,Zuoxiang Peng,Saralees Nadarajah 대한수학회 2008 대한수학회보 Vol.45 No.1
The rate of convergence of the distribution of order statisticsto the corresponding extreme-value distribution may be characterized bythe uniform and total variation metrics. de Haan and Resnick [4] de-rived the convergence rate when the second order generalized regularlyvarying function has second order derivatives. In this paper, based on theproperties of the generalized regular variation and the second order gener-alized variation and characterized by uniform and total variation metrics,the convergence rates of the distribution of the largest order statistic areobtained under weaker conditions.
Study on the Evolution Law of Sandstone Porosity under Soaking-Drying Cycles
Zuosen Luo,Zuoxiang Zhu,Qiao Jiang,Xiaoliang Xu,Daxiang Liu,Meiling Zhou 대한토목학회 2022 KSCE Journal of Civil Engineering Vol.26 No.1
In view of the problem whereby the rock masses in water-level fluctuation zones of reservoir banks are susceptible to deterioration due to soaking-drying cycles, the sandstone of a typical landslide in the Three Gorges Reservoir area is selected as the test object to determine the ion concentration of an immersion solution and rock sample via periodic water-rock microscopic images, quantitative back analysis of the porosity changes caused by the dissolution of rock minerals under soaking-drying cycles, and evaluation of the sandstone porosity evolution. The results show that, 1) in the first two soaking-drying cycles, the generation rate of each ion is relatively high, and after 6 soaking-drying cycles, the ion generation rate tends to remain stable. 2) The volume reduction in calcite is the largest, followed by that in albite and potash feldspar. 3) Small porosity changes result in a considerable decrease in the compressive strength. 4) Sandstone porosity increase leads to an increase in rock pores, which is manifested as a deterioration of the macroscopic rock mechanical properties. Relevant research results could provide a reliable data basis for the study of large-scale reservoir bank slope protection and geological disaster evaluation and prediction.
Shan Jiang,Zuoxiang Zeng,Weilan Xue,Wei Zhang,Zhiyuan Zhou 한국화학공학회 2020 Korean Journal of Chemical Engineering Vol.37 No.9
This study explored the direct esterification of palmitic acid and ethanol using a deep eutectic solvent (DES) as catalyst to produce biodiesel. Three novel deep eutectic solvents (DTAC-PTSA, DTAC-2PTSA, DTAC3PTSA) were successfully prepared by mixing dodecyl trimethyl ammonium chloride (DTAC) and p-toluenesulfonic acid monohydrate (PTSA) in a molar ratio of 1: z (z=1, 2, 3). After testing, DTAC-3PTSA was found to have the best catalytic performance among the three types of DESs and was therefore selected as the catalyst for subsequent experiments. The effects of agitation speed, ethanol to palmitic acid molar ratio (), temperature and catalyst dosage were studied by investigating the change of palmitic acid conversion rate with time under different conditions, respectively. Then, the pseudo-homogeneous (PH) model was utilized to describe the kinetic behavior of this reaction between 328.15-348.15 K and it was found to work well for the experimental data obtained. Moreover, the catalytic performance of DTAC-3PTSA was detected to have no significant change in the cycle test. Therefore, DTAC-3PTSA can be considered as a substitute for traditional catalysts to produce biodiesel and the kinetic data obtained here can be used for further up-scaling study
CONVERGENCE RATE OF EXTREMES FOR THE GENERALIZED SHORT-TAILED SYMMETRIC DISTRIBUTION
Lin, Fuming,Peng, Zuoxiang,Yu, Kaizhi Korean Mathematical Society 2016 대한수학회보 Vol.53 No.5
Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.
Modeling of censored bivariate extremal events
Enkelejd Hashorva,Chengxiu Ling,Zuoxiang Peng 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.3
In this paper we consider the estimation of the coefficient of tail dependence and of smalltail probability under a bivariate randomly censoring mechanism. A new class of generalizedmoment estimators of the coefficient of tail dependence and the estimator of smalltail probability are proposed, respectively. Under the bivariate Hall-type conditions, theasymptotic distributions of these estimators are established. Monte Carlo simulations areperformed and the new estimators are applied to an insurance data-set.
Lin, Fuming,Peng, Zuoxiang,Nadarajah, Saralees Korean Mathematical Society 2008 대한수학회보 Vol.45 No.1
The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.
Kinetics of polyvinyl butyral hydrolysis in ethanol/water solutions
Wenwen Luan,Chunyu Wang,Zuoxiang Zeng,Weilan Xue,Xuelian He,Yu Bai 한국화학공학회 2021 Korean Journal of Chemical Engineering Vol.38 No.9
The hydrolysis kinetics of polyvinyl butyral (PVB) was studied in ethanol/water mixed solvents in the temperature range of 339.15-355.15 K, and a three-step hypothesis was proposed to describe the hydrolysis process. The influences of stirring speed, ethanol content and temperature on the hydrolysis of PVB were investigated, and an induction period (IP) phenomenon was found in the process of PVB hydrolysis. The ethanol content in the mixed solvents has a great influence on IP, which is due to the formation of the two kinds of water-ethanol clusters in the system. Temperature influences the IP by changing the catalytic activity of hydroxylamine hydrochloride (HH) on the hydrolysis of PVB. The shrinking core models with three controlling steps were used to fit the kinetic data, and the results indicate that the model controlled by chemical reaction is suitable to describe the kinetic behavior of PVB hydrolysis.