• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• Genomics & Informatics
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• v.5 no.4
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• pp.168-173
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• 2007

In previous nuclear genomic association studies, Random Forests (RF), one of several up-to-date machine learning methods, has been used successfully to generate evidence of association of genetic polymorphisms with diseases or other phenotypes. Compared with traditional statistical analytic methods, such as chi-square tests or logistic regression models, the RF method has advantages in handling large numbers of predictor variables and examining gene-gene interactions without a specific model. Here, we applied the RF method to find the association between mitochondrial single nucleotide polymorphisms (mtSNPs) and diabetes risk. The results from a chi-square test validated the usage of RF for association studies using mtDNA. Indexes of important variables such as the Gini index and mean decrease in accuracy index performed well compared with chi-square tests in favor of finding mtSNPs associated with a real disease example, type 2 diabetes.

• Structural Engineering and Mechanics
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• v.13 no.1
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• pp.53-74
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• 2002

Composites exhibit larger dispersion in their material properties compared to conventional materials due to larger number of parameters associated with their manufacturing processes. A $C^0$ finite element method has been used for arriving at an eigenvalue problem using higher order shear deformation theory for initial buckling of laminated composite plates. The material properties have been modeled as basic random variables. A mean-centered first order perturbation technique has been used to find the probabilistic characteristics of the buckling loads with different edge conditions. Results have been compared with Monte Carlo simulation, and those available in literature.

• Computers and Concrete
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• v.10 no.5
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• pp.507-521
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• 2012

The capacity design of shear forces is one of the special demands of EC8 by which the ductile behavior of structures is implemented. The aim of capacity design is the formation of plastic hinges without shear failure of the elements. This is achieved by deriving the design shear forces from equilibrium conditions, assuming that plastic hinges, with their possible over-strengths, have been formed in the adjacent joints of the elements. In this equilibrium situation, the parameters (dimensions, material properties, axial forces etc) are random variables. Therefore, the capacity design of shear forces is associated with a probability of non-compliance (probability of failure). In the present study the probability of non-compliance of the shear capacity design in columns is calculated by assuming the basic variables as random variables. Parameters affecting this probability are examined and a modification of the capacity design is proposed, in order to achieve uniformity of the safety level.

• Computers and Concrete
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• v.8 no.6
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• pp.631-645
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• 2011

The capacity design rule for beam-column joints, as adopted by the EC8, forces the formation of the plastic hinges to be developed in beams rather than in columns. This is achieved by deriving the design moments of the columns of a joint from equilibrium conditions, assuming that plastic hinges with their possible overstrengths have been developed in the adjacent beams of the joint. In this equilibrium the parameters (dimensions, material properties, axial forces etc) are, in general, random variables. Hence, the capacity design is associated with a probability of non-compliance (probability of failure). In the present study the probability of non-compliance of the capacity design rule of joints is being calculated by assuming the basic variables as random variables. Parameters affecting this probability are examined and a modification of the capacity design rule for beam-column joints is proposed, in order to achieve uniformity of the safety level.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.743-754
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• 1997

We introduce a class of finite and infinite moving average (MA) sequences of multivariate random vectors exponential marginals. The theory of dependence is used to show that in various cases the class of MA sequences consists of associated random variables. We utilize positive dependence properties to obtain some probability bounds for the multivariate processes.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.595-611
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• 2013

This paper aims to compare three collocation point methods associated with the odd order stochastic response surface method (SRSM) in a systematical and quantitative way. The SRSM with the Hermite polynomial chaos is briefly introduced first. Then, three collocation point methods, namely the point method, the root method and the without origin method underlying the odd order SRSMs are highlighted. Three examples are presented to demonstrate the accuracy and efficiency of the three methods. The results indicate that the condition that the Hermite polynomial information matrix evaluated at the collocation points has a full rank should be satisfied to yield reliability results with a sufficient accuracy. The point method and the without origin method are much more efficient than the root method, especially for the reliability problems involving a large number of random variables or requiring complex finite element analysis. The without origin method can also produce sufficiently accurate reliability results in comparison with the point and root methods. Therefore, the origin often used as a collocation point is not absolutely necessary. The odd order SRSMs with the point method and the without origin method are recommended for the reliability analysis due to their computational accuracy and efficiency. The order of SRSM has a significant influence on the results associated with the three collocation point methods. For normal random variables, the SRSM with an order equaling or exceeding the order of a performance function can produce reliability results with a sufficient accuracy. The order of SRSM should significantly exceed the order of the performance function involving strongly non-normal random variables.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.247-256
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• 2012

In this paper we prove the complete convergence for weighted sums of pairwise negatively quadrant dependent random variables. Some results on identically distributed and negatively associated setting of Liang and Su (1999) are generalized and extended to the pairwise negative quadrant dependence case.