scholarly journals Moment inequality of the minimum for nonnegative negatively orthant dependent random variables

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1475-1481
Author(s):  
Xuejun Wang ◽  
Shijie Wang ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Exponential Inequality ◽  
Moment Inequalities ◽  
Moment Inequality ◽  
Dependent Random Variables ◽  
The Moment

Let {xn,n ? 1} be a sequence of positive numbers and {?n,n ? 1} be a sequence of nonnegative negatively orthant dependent (NOD) random variables satisfying certain distribution conditions. An exponential inequality for the minimum min1?i?n xi?i is given. In addition, the moment inequalities of the minimum (Ek - min1?i?n|xi?i|p)1/p for nonnegative negatively orthant dependent random variables are established, where p > 0 and k = 1,2,..., n. Our results generalize the corresponding ones for independent random variables to the case of negatively orthant dependent random variables.

scholarly journals Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Qunying Wu
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Weighted Sums ◽  
Moment Inequality ◽  
Convergence Theorems ◽  
Dependent Random Variables ◽  
Negatively Dependent Random Variables ◽  
The Moment

Applying to the moment inequality of negatively dependent random variables the complete convergence for weighted sums of sequences of negatively dependent random variables is discussed. As a result, complete convergence theorems for negatively dependent sequences of random variables are extended.

Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process

1984 ◽  
Vol 21 (1) ◽  
pp. 98-107 ◽  
Author(s):  
Minoru Yoshida
Keyword(s):  
Distribution Function ◽  
Stopping Time ◽  
Random Variables ◽  
Secretary Problem ◽  
Independent Random Variables ◽  
Distribution Law ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Random Moment ◽  
The Moment

Before some random moment θ, independent identically distributed random variables x1, · ··, xθ–1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.

scholarly journals On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guodong Xing ◽  
Shanchao Yang
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Exponential Inequality ◽  
Precise Asymptotics ◽  
Dependent Random Variables

The exponential inequality for weighted sums of a class of linearly negative quadrant dependent random variables is established, which extends and improves the corresponding ones obtained by Ko et al. (2007) and Jabbari et al. (2009). In addition, we also give the relevant precise asymptotics.

scholarly journals On Error Bounds for Approximations to Multivariate Distributions II

2002 ◽  
Vol 32 (1) ◽  
pp. 57-69
Author(s):  
Bjørn Sundt ◽  
Raluca Vernic
Keyword(s):  
Error Bounds ◽  
Random Variables ◽  
Independent Random Variables ◽  
Multivariate Distributions ◽  
Dependent Random Variables ◽  
Linear Transforms ◽  
Original Distribution ◽  
Multivariate Bernoulli ◽  
Bernoulli Distributions

AbstractIn the present paper, we study error bounds for approximations to multivariate distributions. In particular, we discuss some general versions of compound multivariate distributions and look at distributions of dependent random variables constructed by linear transforms of independent random variables or vectors. Special attention is paid to the case when the support of the original distribution is restricted. We also look at some applications with multivariate Bernoulli distributions.

A note on the exponential inequality for a class of dependent random variables

2011 ◽  
Vol 40 (1) ◽  
pp. 109-114 ◽  
Author(s):  
Soo Hak Sung ◽  
Patchanok Srisuradetchai ◽  
Andrei Volodin
Keyword(s):  
Random Variables ◽  
Exponential Inequality ◽  
Dependent Random Variables

scholarly journals Φ-moment inequalities for independent and freely independent random variables

2016 ◽  
Vol 270 (12) ◽  
pp. 4558-4596 ◽  
Author(s):  
Yong Jiao ◽  
Fedor Sukochev ◽  
Guangheng Xie ◽  
Dmitriy Zanin
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Moment Inequalities

Some Inequalities of Partial Sums for Negatively Dependent Random Variables

2012 ◽  
Vol 195-196 ◽  
pp. 694-700
Author(s):  
Hai Wu Huang ◽  
Qun Ying Wu ◽  
Guang Ming Deng
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Exponential Inequalities ◽  
Dependent Random Variables ◽  
Probability Inequalities ◽  
Associated Random Variables ◽  
Negatively Dependent Random Variables

The main purpose of this paper is to investigate some properties of partial sums for negatively dependent random variables. By using some special numerical functions, and we get some probability inequalities and exponential inequalities of partial sums, which generalize the corresponding results for independent random variables and associated random variables. At last, exponential inequalities and Bernsteins inequality for negatively dependent random variables are presented.

scholarly journals Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Aiting Shen
Keyword(s):  
Strong Consistency ◽  
Nearest Neighbor ◽  
Type Inequality ◽  
Random Variables ◽  
Independent Random Variables ◽  
Bernstein Type ◽  
Dependent Random Variables ◽  
Bernstein Type Inequality ◽  
Dependent Sequence ◽  
Fixed Design Regression

We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained.

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