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 Performance Degradation in Cross-Eye Jamming Due to Amplitude/Phase Instability between Jammer Antennas

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5027
Author(s):  
Je-An Kim ◽  
Joon-Ho Lee
Keyword(s):  
Performance Analysis ◽  
Phase Difference ◽  
Taylor Expansion ◽  
Amplitude Ratio ◽  
Random Variables ◽  
Performance Degradation ◽  
Analytical Performance ◽  
Phase Instability ◽  
Gaussian Random Variables ◽  
First Order

Cross-eye gain in cross-eye jamming systems is highly dependent on amplitude ratio and the phase difference between jammer antennas. It is well known that cross-eye jamming is most effective for the amplitude ratio of unity and phase difference of 180 degrees. It is assumed that the instabilities in the amplitude ratio and phase difference can be modeled as zero-mean Gaussian random variables. In this paper, we not only quantitatively analyze the effect of amplitude ratio instability and phase difference instability on performance degradation in terms of reduction in cross-eye gain but also proceed with analytical performance analysis based on the first order and second-order Taylor expansion.

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.

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