scholarly journals New-type Hoeffding’s inequalities and application in tail bounds

2021 ◽  
Vol 5 (1) ◽  
pp. 248-261
Author(s):  
Pingyi Fan ◽  
Keyword(s):  
Information Processing ◽  
Random Variables ◽  
Order Moment ◽  
First Order ◽  
Hoeffding’S Inequalities ◽  
New Type ◽  
Hoeffding’S Inequality ◽  
Hoeffding Inequality ◽  
Moments Of Random Variables ◽  
Refined Version

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz [<a href="#1">1</a>]. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refined version by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.

A Modified High-Order Moment Method Based on the Normal Transformation Polynomial

2011 ◽  
Vol 261-263 ◽  
pp. 873-877
Author(s):  
Wei Li
Keyword(s):  
Moment Method ◽  
Random Variables ◽  
High Order ◽  
Order Moment ◽  
Test Problems ◽  
Third Order ◽  
High Order Moment ◽  
Polynomial Coefficients ◽  
Normal Transformation ◽  
Moments Of Random Variables

Normal transformation technique is often used in practical probabilistic analysis in structural or civil engineering especially when multivariate random variables with the probabilistic characteristics expressed using only statistical moments are involved. In this paper, a modified high-order moment method(MHOM) is given based on the polynomial coefficients of a third-order normal transformation polynomial (NTP) using the first four central moments of random variables having unknown distributions. The present high-order moment method is introduced into several typical test problems having unknown distributions are available. Since it needs neither the computation of derivatives nor iteration, and since it is unnecessary to know the probability distribution of the basic random variables, the present method should be practical in actual reliability problems. Applications to several typical examples have helped to elucidate the successful working of the present MHOM.

scholarly journals Fully degenerate Bell polynomials associated with degenerate Poisson random variables

2021 ◽  
Vol 19 (1) ◽  
pp. 284-296
Author(s):  
Hye Kyung Kim
Keyword(s):  
Random Variables ◽  
Random Variable ◽  
Combinatorial Identities ◽  
Bell Polynomials ◽  
Poisson Random Variable ◽  
Central Moments ◽  
Special Polynomials ◽  
Special Numbers And Polynomials ◽  
New Type ◽  
Two Parameters

Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.

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.

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

scholarly journals Functional ASP with Intensional Sets: Application to Gelfond-Zhang Aggregates

2018 ◽  
Vol 18 (3-4) ◽  
pp. 390-405 ◽  
Author(s):  
PEDRO CABALAR ◽  
JORGE FANDINNO ◽  
LUIS FARIÑAS DEL CERRO ◽  
DAVID PEARCE
Keyword(s):  
Binary Operation ◽  
Compositional Semantics ◽  
First Order ◽  
Simple Addition ◽  
Logical Language ◽  
Extended Approach ◽  
Logical Term ◽  
New Type ◽  
The One ◽  
Logical Treatment

AbstractIn this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions (${\rm QEL}^=_{\cal F}$). Then, we proceed to incorporate a new kind of logical term,intensional set(a construct commonly used to denote the set of objects characterised by a given formula), and to extend${\rm QEL}^=_{\cal F}$semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count,sum,maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the${\rm QEL}^=_{\cal F}$interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to definesumin terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the${\cal A}\mathit{log}$language, when we restrict to that syntactic fragment.

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

A METAMAGNETIC QUANTUM CRITICAL ENDPOINT IN Sr3Ru2O7

2002 ◽  
Vol 16 (20n22) ◽  
pp. 3258-3264 ◽  
Author(s):  
S. A. GRIGERA ◽  
A. P. MACKENZIE ◽  
A. J. SCHOFIELD ◽  
S. R. JULIAN ◽  
G. G. LONZARICH
Keyword(s):  
Quantum Critical Point ◽  
Point Of View ◽  
Zero Temperature ◽  
Tuning Parameters ◽  
First Order ◽  
End Point ◽  
Fundamental Point ◽  
New Type ◽  
Quantum Critical ◽  
The Magnetic Field

In this paper, we discuss the concept of a metamagnetic quantum critical end-point, consequence of the depression to zero temperature of a critical end-point terminating a line of first order first transitions. This new type of quantum critical point (QCP) is interesting both from a fundamental point of view: a study of a symmetry conserving QCP, and because it opens the possibility of the use of symmetry breaking tuning parameters, notably the magnetic field. In addition, we discuss the experimental evidence for the existence of such a QCP in the bilayer ruthenate Sr3Ru2O7.

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