Stolarsky’s inequality for Choquet-like expectation

2016 ◽  
Vol 66 (5) ◽  
Author(s):  
Hamzeh Agahi ◽  
Radko Mesiar
Keyword(s):  
Probability Theory ◽  
Fundamental Concept ◽  
Minkowski’S Inequality ◽  
Sugeno Integral ◽  
Statistics And Probability ◽  
Choquet Expectation ◽  
Generalized Probability

AbstractExpectation is the fundamental concept in statistics and probability. As two generalizations of expectation, Choquet and Choquet-like expectations are commonly used tools in generalized probability theory. This paper considers the Stolarsky inequality for two classes of Choquet-like integrals. The first class generalizes the Choquet expectation and the second class is an extension of the Sugeno integral. Moreover, a new Minkowski’s inequality without the comonotonicity condition for two classes of Choquet-like integrals is introduced. Our results significantly generalize the previous results in this field. Some examples are given to illustrate the results.

scholarly journals A new proof for the generalized law of large numbers under Choquet expectation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jing Chen ◽  
Zengjing Chen
Keyword(s):  
Probability Theory ◽  
Law Of Large Numbers ◽  
Moment Condition ◽  
Large Numbers ◽  
Choquet Expectation ◽  
The Law ◽  
Linear Probability ◽  
First Moment ◽  
Independent And Identically Distributed

Abstract In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.

Descriptive Statistics and Probability Theory

1973 ◽  
Vol 57 (401) ◽  
pp. 236
Author(s):  
S. Letchford ◽  
Robert A. Barks
Keyword(s):  
Probability Theory ◽  
Descriptive Statistics ◽  
Statistics And Probability

scholarly journals Comparison of Results Obtained by Two Methods of Surface Mapping

2020 ◽  
Vol 16 (1) ◽  
pp. 1-10
Author(s):  
Jozef Melcer ◽  
Eva Merčiaková ◽  
Peter Pisca
Keyword(s):  
Probability Theory ◽  
Primary Source ◽  
Data Sets ◽  
Surface Mapping ◽  
Kinematic Excitation ◽  
The Road ◽  
Comparison Of Results ◽  
Statistics And Probability ◽  
Important Input ◽  
On The Road

AbstractConsidering that the unevenness of the road surface is the primary source of the kinematic excitation of the vehicle, it is necessary to map the unevenness, and then to describe it mathematically. The data sets thus obtained represent an important input for numerical simulations of the motion of vehicles on the road. This paper deals with the analysis and comparison of results from two methods of mapping the surface of the road - exact levelling and spatial scanning. The obtained results are evaluated qualitatively and quantitatively by methods of mathematical statistics and probability theory.

Uncertainty of Integral System Safety in Enginering

2021 ◽  
Author(s):  
Kalman Ziha
Keyword(s):  
Probability Theory ◽  
System Reliability ◽  
Probability Distributions ◽  
Conditional Entropy ◽  
System State ◽  
System Safety ◽  
Integral System ◽  
Statistics And Probability ◽  
System Uncertainties ◽  
System States

Abstract The probabilistic safety analysis evaluates system reliability and failure probability by using statistics and probability theory but it cannot estimate the system uncertainties due to variabilities of system state probabilities. The article firstly resumes how the information entropy expresses the probabilistic uncertainties due to unevenness of probability distributions of system states. Next it argues that the conditional entropy with respect to system operational and failure states appropriately describes system redundancy and robustness, respectively. Finally the article concludes that the joint probabilistic uncertainties of reliability, redundancy and robustness defines the integral system safety. The concept of integral system safety allows more comprehensive definitions of favorable system functional properties, configuration evaluation, optimization and decision making in engineering.

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