Exponential probability inequality for $$m$$ m -END random variables and its applications

Metrika ◽  
2015 ◽  
Vol 79 (2) ◽  
pp. 127-147 ◽  
Author(s):  
Xuejun Wang ◽  
Yi Wu ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Probability Inequality ◽  
End Random Variables ◽  
Exponential Probability

NEW EXPONENTIAL PROBABILITY INEQUALITY AND COMPLETE CONVERGENCE FOR F-LNQD RANDOM VARIABLES SEQUENCE WITH APPLICATION TO AR(1)MODEL GENERATED BY F-LNQD ERRORS

2021 ◽  
Vol 21 (2) ◽  
pp. 437-448
Author(s):  
NADJIA AZZEDINE ◽  
AMINA ZEBLAH ◽  
SAMIR BENAISSA
Keyword(s):  
Complete Convergence ◽  
Random Variables ◽  
Tail Probability ◽  
Probability Inequality ◽  
Autoregressive Processes ◽  
Probability Inequalities ◽  
First Order ◽  
Probability And Statistics ◽  
Exponential Probability

The exponential probability inequalities have been important tools in probability and statistics. In this paper, we prove a new tail probability inequality for the distri-butions of sums of conditionally linearly negative quadrant dependent (F-LNQD , in short) random variables, and obtain a result dealing with conditionally complete con-vergence of first-order autoregressive processes with identically distributed (F-LNQD) innovations.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

scholarly journals Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Chen ◽  
Zhihui Qu
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Random Sums ◽  
Tail Probabilities ◽  
Precise Large Deviations ◽  
Surplus Process ◽  
End Random Variables ◽  
Renewal Risk

We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

scholarly journals On the Bahadur representation of sample quantiles for widely orthant dependent sequences

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1333-1343 ◽  
Author(s):  
Wenzhi Yang ◽  
Tingting Liu ◽  
Xuejun Wang ◽  
Shuhe Hu
Keyword(s):  
Random Variables ◽  
Bahadur Representation ◽  
Negatively Associated ◽  
Statistics And Probability ◽  
Na Random Variables ◽  
End Random Variables ◽  
Widely Orthant Dependent ◽  
Na Sequences ◽  
Nod Sequence ◽  
Sample Quantiles

It can be found that widely orthant dependent (WOD) random variables are weaker than extended negatively orthant dependent (END) random variables, while END random variables are weaker than negatively orthant dependent (NOD) and negatively associated (NA) random variables. In this paper, we investigate the Bahadur representation of sample quantiles based on WOD sequences. Our results extend the corresponding ones of Ling [N.X. Ling, The Bahadur representation for sample quantiles under negatively associated sequence, Statistics and Probability Letters 78(16) (2008), 2660-2663], Xu et al. [S.F. Xu, L. Ge, Y. Miao, On the Bahadur representation of sample quantiles and order statistics for NA sequences, Journal of the Korean Statistical Society 42(1) (2013), 1-7] and Li et al. [X.Q. Li, W.Z. Yang, S.H. Hu, X.J. Wang, The Bahadur representation for sample quantile under NOD sequence, Journal of Nonparametric Statistics 23(1) (2011), 59-65] for the case of NA sequences or NOD sequences.

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