A general inequality for the rejection probability of the sprt

1987 ◽  
Vol 6 (4) ◽  
pp. 289-302
Author(s):  
Wolfgang Stadje
Keyword(s):  
General Inequality ◽  
Rejection Probability

Linking Input Inequality and Outcome Inequality

2021 ◽  
Vol 50 (3) ◽  
pp. 944-1005
Author(s):  
Guillermina Jasso
Keyword(s):  
General Inequality ◽  
Fast Growing ◽  
Fundamental Theorems ◽  
Outcome Function

Inequality often appears in linked pairs of variables. Examples include schooling and income, income and consumption, and wealth and happiness. Consider the famous words of Veblen: “wealth confers honor.” Understanding inequality requires understanding input inequality, outcome inequality, and the relation between the two—in both inequality between persons and inequality between subgroups. This article contributes to the methodological toolkit for studying inequality by developing a framework that makes explicit both input inequality and outcome inequality and by addressing three main associated questions: (1) How do the mechanisms for generating and altering inequality differ across inputs and outcomes? (2) Which have more inequality—inputs or outcomes? (3) Under what conditions, and by what mechanisms, does input inequality affect outcome inequality? Results include the following: First, under specified conditions, distinctive mechanisms govern inequality in inputs and inequality in outcomes. Second, input inequality and outcome inequality can be the same or different; if different, whether inequality is greater among inputs or outcomes depends on the configuration of outcome function, types of inputs, distributional form of and inequality in cardinal inputs, and number of and associations among inputs. Third, the link between input inequality and outcome inequality is multiform; it can be nonexistent, linear, or nonlinear, and if nonlinear, it can be concave or convex. More deeply, this work signals the formidable empirical challenges in studying inequality, but also the fast growing toolbox. For example, even if the outcome distribution is difficult to derive, fundamental theorems on the variance make it possible to analyze the input–outcome inequality connection. Similarly, within specified distributions, the general inequality parameter makes it possible to express results in terms of both measures of overall inequality and measures of subgroup inequality.

Study on Sequential Compliance Method Influenced by Shape Parameter of Weibull Distribution

2011 ◽  
Vol 189-193 ◽  
pp. 4361-4364 ◽  
Author(s):  
Hong Liang Lou ◽  
Xing Lin Li ◽  
Xian Zhao Xu ◽  
Yang Ping Zhang ◽  
Zhong Hua Yu
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Weibull Distributions ◽  
Simulation Test ◽  
Consumer’S Risk ◽  
Producer’S Risk ◽  
Rejection Probability

When sequential compliance method is used for Weibull distributions, the shape parameter is usually considered to be fixed. However, because of the life of products are determined by many factors, the shape parameter is variational in practice, that is to say, the shape parameter in the criterions is different from that in the practice. In this paper, the changes of acceptance and rejection probability are researched by the influence of shape parameter changes. Finally, by means of simulation test, changes on the shape parameter affecting on the probability of acceptance and rejection are quantitatively analyzed. As a result, the larger the gap on the shape parameter in the criterions and in the practice is, the larger the gap on the producer’s risk and the consumer’s risk.

scholarly journals Rejection Sampling Revisit: How to Choose Parameters in Lattice-Based Signature

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Zhongxiang Zheng ◽  
Anyu Wang ◽  
Lingyue Qin
Keyword(s):  
Uniform Distribution ◽  
Sampling Theorem ◽  
New Method ◽  
Security Level ◽  
Rejection Sampling ◽  
Forgery Attack ◽  
Rejection Probability ◽  
Standardization Process ◽  
Security Levels ◽  
Security Bound

Rejection sampling technology is a core tool in the design of lattice-based signatures with ‘Fiat–Shamir with Aborts’ structure, and it is related to signing efficiency and signature, size as well as security. In the rejection sampling theorem proposed by Lyubashevsky, the masking vector of rejection sampling is chosen from discrete Gaussian distribution. However, in practical designs, the masking vector is more likely to be chosen from bounded uniform distribution due to better efficiency and simpler implementation. Besides, as one of the third-round candidate signatures in the NIST postquantum cryptography standardization process, the 3rd round version of CRYSTALS-Dilithium has proposed a new method to decrease the rejection probability in order to achieve better efficiency and smaller signature size by decreasing the number of nonzero coefficients of the challenge polynomial according to the security levels. However, it is seen that small entropies in this new method may lead to higher risk of forgery attack compared with former schemes proposed in its 2nd version. Thus, in this paper, we first analyze the complexity of forgery attack for small entropies and then introduce a new method to decrease the rejection probability without loss of security including the security against forgery attack. This method is achieved by introducing a new rejection sampling theorem with tighter bound by utilizing Rényi divergence where masking vector follows uniform distribution. By observing large gaps between the security claim and actual security bound in CRYSTALS-Dilithium, we propose two series of adapted parameters for CRYSTALS-Dilithium. The first set can improve the efficiency of the signing process in CRYSTALS-Dilithium by factors of 61.7 %  and  41.7 % , according to the security levels, and ensure the security against known attacks, including forgery attack. And, the second set can reduce the signature size by a factor of 14.09 % with small improvements in efficiency at the same security level.

scholarly journals Weighted Opial inequalities

2002 ◽  
Vol 33 (1) ◽  
pp. 83-92
Author(s):  
J. J. Koliha ◽  
J. Pecaric
Keyword(s):  
Difference Equations ◽  
Fractional Derivatives ◽  
Kluwer Acad ◽  
General Inequality ◽  
Opial’S Inequality ◽  
Opial's Inequality

This paper presents a class of very general weighted Opial type inequalities. The notivation comes from the monograph of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, Kluwer Acad., Dordrecht 1995) and the work of Anastassiou and Pecaric (J. Math. Anal. Appl. 239 (1999), 402-418).  Assuming only a very general inequality, we extend the latter paper in several directions.  A new result generalizing the original Opial's inequality is obtained, and applications to fractional derivatives are given.

Another General Inequality for Bi-warped Products in Kenmotsu Manifolds

2019 ◽  
Author(s):  
Monia Fouad Naghi ◽  
Siraj Uddin ◽  
Mića S. Stanković
Keyword(s):  
Warped Products ◽  
General Inequality ◽  
Kenmotsu Manifolds

A Fast and Robust Algorithm for General Inequality/Equality Constrained Minimum-Time Problems

1999 ◽  
Vol 121 (3) ◽  
pp. 337-345 ◽  
Author(s):  
B. J. Driessen ◽  
N. Sadegh ◽  
G. G. Parker ◽  
G. R. Eisler
Keyword(s):  
Maximum Principle ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Joint Angle ◽  
Minimum Time ◽  
Robotic Arm ◽  
General Inequality ◽  
Constrained Problems ◽  
Ill Conditioning ◽  
Minimum Time Problems

This work has developed a new robust and reliable O(N) algorithm for solving general inequality/equality constrained minimum-time problems. To our knowledge, no one has ever applied an O(N) algorithm for solving such minimum time problems. Moreover, the algorithm developed here is new and unique and does not suffer the inevitable ill-conditioning problems that pre-existing O(N) methods for inequality-constrained problems do. Herein we demonstrate the new algorithm by solving several cases of a tip path constrained three-link redundant robotic arm problem with torque bounds and joint angle bounds. Results are consistent with Pontryagin’s Maximum Principle. We include a speed/robustness/complexity comparison with a sequential quadratic programming (SQP) code. Here, the O(N) complexity and the significant speed, robustness, and complexity improvements over an SQP code are demonstrated. These numerical results are complemented with a rigorous theoretical convergence proof of the new O(N) algorithm.

Study of Sequential Sampling Method for Weibull Distribution

2011 ◽  
Vol 291-294 ◽  
pp. 2195-2198 ◽  
Author(s):  
Xian Zhao Xu ◽  
Hong Liang Lou ◽  
Xing Lin Li
Keyword(s):  
Weibull Distribution ◽  
Sampling Method ◽  
Shape Parameter ◽  
Sequential Sampling ◽  
Acceptance Probability ◽  
Distribution Shape ◽  
Rejection Probability

When sequential sampling method based on MTTF is applied to weibull distribution, shape parameter is considered to be fixed. But, shape parameter in criterions or references is different from that in practice. According to sequential sampling method, with the shape parameter changing, changes of acceptance probability and rejection probability are studied. Finally, the result of simulation evaluating shows that the method of sequential sampling method is feasible and reasonable.

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