• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.627-634
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• 2001

Under contamination, Bahadur representations with a strong remainder term are derived for random central order statistics with a prescribed limiting rank, and asymptotic normalities for these statistics of truncated and contaminated data are proved, with a suitable limiting rank. From these results, an application to the fixed-width confidence interval problem is available.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.477-493
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• 2017

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random variables like order statistics and lower record values. With this definition we give simple expressions for single and product moments of dual generalized order statistics from Dagum distribution. The results for order statistics and lower records are deduced from the relations derived and some computational works are also carried out. Further, a characterizing result of this distribution on using the conditional moment of the dual generalized order statistics is discussed. These recurrence relations enable computation of the means, variances and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, skewness and kurtosis of order statistics and record values of the Dagum distribution.

• Advances in Computational Design
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• v.2 no.3
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).

• Progress in Medical Physics
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• v.23 no.2
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• pp.81-90
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• 2012

The effect of setup uncertainties on CTV dose and the correlation between setup uncertainties and setup margin were evaluated by Monte Carlo based numerical simulation. Patient specific information of IMRT treatment plan for rectal cancer designed on the VARIAN Eclipse planning system was utilized for the Monte Carlo simulation program including the planned dose distribution and tumor volume information of a rectal cancer patient. The simulation program was developed for the purpose of the study on Linux environment using open source packages, GNU C++ and ROOT data analysis framework. All misalignments of patient setup were assumed to follow the central limit theorem. Thus systematic and random errors were generated according to the gaussian statistics with a given standard deviation as simulation input parameter. After the setup error simulations, the change of dose in CTV volume was analyzed with the simulation result. In order to verify the conventional margin recipe, the correlation between setup error and setup margin was compared with the margin formula developed on three dimensional conformal radiation therapy. The simulation was performed total 2,000 times for each simulation input of systematic and random errors independently. The size of standard deviation for generating patient setup errors was changed from 1 mm to 10 mm with 1 mm step. In case for the systematic error the minimum dose on CTV $D_{min}^{stat{\cdot}}$ was decreased from 100.4 to 72.50% and the mean dose $\bar{D}_{syst{\cdot}}$ was decreased from 100.45% to 97.88%. However the standard deviation of dose distribution in CTV volume was increased from 0.02% to 3.33%. The effect of random error gave the same result of a reduction of mean and minimum dose to CTV volume. It was found that the minimum dose on CTV volume $D_{min}^{rand{\cdot}}$ was reduced from 100.45% to 94.80% and the mean dose to CTV $\bar{D}_{rand{\cdot}}$ was decreased from 100.46% to 97.87%. Like systematic error, the standard deviation of CTV dose ${\Delta}D_{rand}$ was increased from 0.01% to 0.63%. After calculating a size of margin for each systematic and random error the "population ratio" was introduced and applied to verify margin recipe. It was found that the conventional margin formula satisfy margin object on IMRT treatment for rectal cancer. It is considered that the developed Monte-carlo based simulation program might be useful to study for patient setup error and dose coverage in CTV volume due to variations of margin size and setup error.