• Communications for Statistical Applications and Methods
• /
• v.19 no.1
• /
• pp.85-95
• /
• 2012

In this paper we define extended negative quadrant dependence which is weaker negative quadrant dependence and show conditions for having extended negative quadrant dependence property. We also derive generalized Farlie-Gumbel-Morgenstern uniform distributions that possess the extended quadrant dependence property.

• Honam Mathematical Journal
• /
• v.36 no.4
• /
• pp.767-775
• /
• 2014

In this paper we define the extended conditional negative quadrant dependence and generalize the conditional Borel-Cantelli lemma of B.L.S. Prakasa Rao(2012) to the case of pairwise extended conditionally negative quadrant dependence.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.163-171
• /
• 2013

By extending the negatively quadrant dependence, the paper puts forth the concept of extended negative quadrant dependence. A generalization of the second Borel-Cantelli lemma is obtained under extended negative quadrant dependence. Some applications are also introduced.

• Communications of the Korean Mathematical Society
• /
• v.11 no.3
• /
• pp.831-839
• /
• 1996

In the last years there has been growing interest in concepts of positive (negative) dependence of stochastic processes such that concepts are considerable us in deriving inequalities in probability and statistics. Lehmann [7] introduced various concepts of positive(negative) dependence in the bivariate case. Stronger notions of bivariate positive(negative) dependence were later developed by Esary and Proschan [6]. Ahmed et al.[2], and Ebrahimi and Ghosh[5] obtained multivariate versions of various positive(negative) dependence as described by Lehmann[7] and Esary and Proschan[6]. Concepts of positive(negative) dependence for random variables have subsequently been extended to stochastic processes in different directions by many authors.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.367-379
• /
• 2002

We introduce a new concept of $\theta$ conditionally independent and positive and negative dependence of bivariate stochastic processes and their corresponding hitting times. We have further extended this theory to stronger conditions of dependence similar to those in the literature of positive and negative dependence and developed theorems which relate these conditions. Finally we are given some examples to illustrate these concepts.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.755-768
• /
• 1997

In this paper we introduce a new concept of negative dependence of multivariate random variables. This concept is weaker than the negative orthant dependence(NOD) but it enjoys some properties and preservation results of NOD.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.795-805
• /
• 2011

In this paper, we study a family of continuous bivariate distributions that possesses the negative quadrant dependence property and the generalized negatively quadrant dependent F-G-M copula. We also develop the partial ordering of this new parametric family of negative quadrant dependent distributions.

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.689-699
• /
• 2010

We discuss in this paper the notions of extended negative quadrant dependence and its properties. We study a class of bivariate uniform distributions having extended negative quadrant dependence, which is derived by generalizing the uniform representation of a well-known Farlie-Gumbel-Morgenstern distribution. Finally, we also study the limit behavior on the extended negative quadrant dependence.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.4
• /
• pp.783-793
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.161-168
• /
• 2005

In this paper, we obtain strong law of large numbers for linear process generated by asymptotically linear negative quadrant dependence processes.