Probability inequalities for sums of NSD random variables and applications

2018 ◽  
Vol 49 (2) ◽  
pp. 281-306
Author(s):  
Ting Cai ◽  
Hong Chang Hu
Keyword(s):  
Random Variables ◽  
Probability Inequalities ◽  
Nsd Random Variables

Some remarks on probability inequalities for sums of bounded convex random variables

1975 ◽  
Vol 12 (1) ◽  
pp. 155-158 ◽  
Author(s):  
M. Goldstein
Keyword(s):  
Convex Function ◽  
Exponential Convergence ◽  
Random Variables ◽  
Upper Bounds ◽  
Independent Random Variables ◽  
Probability Inequalities ◽  
Continuous Convex Function ◽  
Bounded Convex

Let X1, X2, · ··, Xn be independent random variables such that ai ≦ Xi ≦ bi, i = 1,2,…n. A class of upper bounds on the probability P(S−ES ≧ nδ) is derived where S = Σf(Xi), δ > 0 and f is a continuous convex function. Conditions for the exponential convergence of the bounds are discussed.

Probability inequalities for continuous unimodal random variables with finite support

1988 ◽  
Vol 17 (10) ◽  
pp. 3505-3519
Author(s):  
Dean M. Young ◽  
John W. Seaman ◽  
Danny W. Turner ◽  
Virgil R. Marco
Keyword(s):  
Random Variables ◽  
Finite Support ◽  
Probability Inequalities
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