• 충청수학회지
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• 제29권3호
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• pp.477-489
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• 2016

The purpose of this paper is to establish the complete moment convergence and the integrability of supremum for weighted sums of pairwise negatively quadrant dependent random variables satisfying stochastically dominating condition.

• 충청수학회지
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• 제24권4호
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• pp.783-793
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• 2011

In this paper we introduce the concept of extended linear negative quadrant dependence and obtain some exponential inequalities, complete convergence and almost sure convergence for extended linear negative quadrant dependent random variables.

• 대한수학회논문집
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• 제9권4호
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• pp.951-959
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• 1994

A sequence ${X_j : j \geq 1}$ of random variables is said to be pairwise positive quadrant dependent (pairwise PQD) if for any real $r-i,r_j$ and $i \neq j$ $$ P{X_i > r_i,X_j > r_j} \geq P{X_i > r_i}P{X_j > r_j} $$ (see [8]) and a sequence ${X_j : j \geq 1}$ of random variables is said to be associated if for any finite collection ${X_{i(1)},...,X_{j(n)}}$ and any real coordinatewise nondecreasing functions f,g on $R^n$ $$ Cov(f(X_{i(1)},...,X_{j(n)}),g(X_{j(1)},...,X_{j(n)})) \geq 0, $$ whenever the covariance is defined (see [6]). Instead of association Cox and Grimmett's [4] original central limit theorem requires only that positively linear combination of random variables are PQD (cf. Theorem $A^*$).

• 대한수학회보
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• 제57권6호
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• pp.1451-1473
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• 2020

Widely orthant dependence (WOD, in short) is a special dependence structure. In this paper, by using the probability inequalities and moment inequalities for WOD random variables, we study the L_p convergence and complete convergence for the partial sums respectively under the conditions of RCI(α), SRCI(α) and R-h-integrability. We also give an application to nonparametric regression models based on WOD errors by using the L_p convergence that we obtained. Finally we carry out some simulations to verify the validity of our theoretical results.

• Communications for Statistical Applications and Methods
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• 제21권3호
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• pp.245-251
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• 2014

Two exponential inequalities are established for a wide class of general weakly dependent sequences of random variables, called ${\psi}$-weakly dependent process which unify weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The ${\psi}$-weakly dependent process includes, for examples, stationary ARMA processes, bilinear processes, and threshold autoregressive processes, and includes essentially all classes of weakly dependent stationary processes of interest in statistics under natural conditions on the process parameters. The two exponential inequalities are established on more general conditions than some existing ones, and are proven in simpler ways.

• 대한수학회지
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• 제43권6호
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• pp.1325-1338
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences of negatively orthant dependent random variables ${X_n,\;n{\geq}1}$, the conditions for strong law of large number of ${\sum}^{k_n}_{i=1}a_{ni}X_i$ are given. Both cases $k_n{\uparrow}{\infty}\;and\;k_n={\infty}$ are treated.

• 대한수학회지
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• 제41권5호
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• pp.883-894
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• 2004

We discuss in this paper the strong convergence for weighted sums of negative associated (in abbreviation: NA) arrays. Meanwhile, the central limit theorem for weighted sums of NA variables and linear process based on NA variables is also considered. As corollary, we get the results on iid of Li et al. ([10]) in NA setting.

• 호남수학학술지
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• 제21권1호
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• pp.149-156
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• 1999

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

• 대한수학회논문집
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• 제19권4호
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• pp.765-773
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• 2004

In this paper we define the notion of asymptotically quadrant independent random field and derive the strong laws of large numbers for this random field.

• 제어로봇시스템학회논문지
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• 제8권10호
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• pp.847-850
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• 2002

Stochastic process analysis is often based on Monte Carlo simulations. As a more rigorous alternative, a deterministic algorithm based on numerical integration is proposed in this paper. which calculates the probability distributions of dependent random variables using the results of simulation with grid points of independent random variables. For performance evaluation, the proposed algorithm is applied to an example problem which can be analytically solved. and the result is compared with that of Monte Carlo simulation. The proposed algorithm is suitable for general process simulation problems with a few independent random variables, and expected to be applicable to areas such as safety analysis and quality control.