scholarly journals Imprecise random variables, random sets, and Monte Carlo simulation

2016 ◽  
Vol 78 ◽  
pp. 252-264 ◽  
Author(s):  
Thomas Fetz ◽  
Michael Oberguggenberger
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Random Variables ◽  
Random Sets

scholarly journals Monte Carlo sampling processes and incentive compatible allocations in large economies

2020 ◽  
Author(s):  
Peter J. Hammond ◽  
Lei Qiao ◽  
Yeneng Sun
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Incentive Compatibility ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Econ Theory ◽  
Monte Carlo Sampling ◽  
Link Type ◽  
Stochastic Framework ◽  
Almost All

Abstract Monte Carlo simulation is used in Hammond and Sun (Econ Theory 36:303–325, 2008. 10.1007/s00199-007-0279-7) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This leads to a necessary and sufficient condition for the classical law of large numbers to hold in a general Hilbert space. Applying this analysis to large economies with asymmetric information shows that the conflict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, following some similar results in McLean and Postlewaite (Econometrica 70:2421–2453, 2002) and Sun and Yannelis (J Econ Theory 134:175–194, 2007. 10.1016/j.jet.2006.03.001).

Analysis of RC Member’s Reliability Subjected to Eccentric Compression Based on Monte Carlo Simulation

2014 ◽  
Vol 487 ◽  
pp. 465-469
Author(s):  
Wen Feng Duan ◽  
Chang Liu
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reinforced Concrete ◽  
Concrete Strength ◽  
Random Variables ◽  
Structural Member ◽  
Eccentric Compression ◽  
Compression Members ◽  
Geometric Size ◽  
Compression Member

Reinforced concrete eccentric compression member is one of the most common structural member. Eccentric compression members are divided into large eccentric compression members and small eccentric compression members. Uncertainty of calculation, geometric size and concrete strength were considered as random variables, the reliability of eccentric compression members were discussed by monte carlo simulation.

Reliability Optimization Design of Gear Box

2011 ◽  
Vol 284-286 ◽  
pp. 2509-2512
Author(s):  
Wen Hui Mo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Material Properties ◽  
Optimization Design ◽  
Random Variables ◽  
Reliability Optimization ◽  
Objective Functions ◽  
Feasible Method ◽  
Reliability Calculation ◽  
Gear Box

Geometry parameters, material properties and applied loads of the gear box are regarded as normal random variables. A model of reliability optimization design of the gear box is introduced. Two objective functions are selected. The Monte Carlo simulation of reliability calculation is presented. With rapid increasing of the speed of CPU, it is a feasible method. The optimization effect is very good.

Reliability Assessment with Fuzzy Random Variables Using Interval Monte Carlo Simulation

2013 ◽  
Vol 29 (3) ◽  
pp. 208-220 ◽  
Author(s):  
Ehsan Jahani ◽  
Rafi L. Muhanna ◽  
Mohsen A. Shayanfar ◽  
Mohammad A. Barkhordari
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Assessment ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

Monte Carlo Simulation of Reliability for Gear

2011 ◽  
Vol 268-270 ◽  
pp. 42-45 ◽  
Author(s):  
Wen Hui Mo
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Fatigue Strength ◽  
Random Variables ◽  
Random Variable ◽  
Accurate Solution ◽  
Bending Fatigue ◽  
Simulation Based ◽  
Production Errors

Production errors, material properties and applied loads of the gear are stochastic .Considering the influence of these stochastic factors, reliability of gear is studied. The sensitivity analysis of random variable can reduce the number of random variables. Simulating random variables, a lot of samples are generated. Using the Monte Carlo simulation based on the sensitivity analysis, reliabilities of contacting fatigue strength and bending fatigue strength can be obtained. The Monte Carlo simulation approaches the accurate solution gradually with the increase of the number of simulations. The numerical example validates the proposed method.

The Distribution of Microcontact Area, Load, Pressure, and Flash Temperature Under the Greenwood-Williamson Model

1988 ◽  
Vol 110 (1) ◽  
pp. 106-111 ◽  
Author(s):  
J. I. McCool
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Contact Area ◽  
Random Variables ◽  
Area Fraction ◽  
Real Contact Area ◽  
Flash Temperature ◽  
Load Pressure ◽  
Average Behavior ◽  
Real Contact

Microcontact models provide average values of the random interfacial load, area and pressure between rough contacting surfaces. They do not provide a measure of the variability about that average. Events of tribological importance, however, are likely to be dependent on extreme rather than average behavior conditions. In this paper Monte Carlo simulation is used to determine the 75th and 90th percentiles of three dimensionless random variables as a function of the dimensionless separation of two contacting rough surfaces. These values may be used to determine the corresponding percentiles under the Greenwood-Williamson microcontact model of the distributions of 1) real contact area fraction, 2) the radius of the microcontact area, 3) microcontact load, 4) the maximum microcontact pressure and 5) the asperity flash temperature under low speed sliding conditions. A numerical example illustrates the computations.

Effects of Soil Properties Uncertainty on Reliability Index of Slope

2011 ◽  
Vol 250-253 ◽  
pp. 1947-1950
Author(s):  
Bo Han ◽  
Hong Jian Liao ◽  
Hang Zhou Li ◽  
Zheng Hua Xiao
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Slope Stability ◽  
Soil Properties ◽  
Normal Distribution ◽  
Reliability Index ◽  
Random Variables ◽  
Simulation Method ◽  
Soil Parameters ◽  
Monte Carlo Simulation Method

A probabilistic analysis procedure and related algorithms were based on the Monte Carlo simulation method that considers the variability of soil properties in this paper. A homogenous slope example provide insight into the effects of uncertainty due to the variability of soil properties on slope stability .Taking soil parameters cohesion c, friction angle, gravity γ as the basic random variables, the reliability index are calculated using Monte Carlo simulation method taking into account the uncertainties of these basic random variables. The calculated results are compared for four recognized methods of slope stability, which are Ordinary method, simplified Bishop method, simplified Janbu method and Morgenstern Price method. And the influence of soil parameters’ probability distribution model (i.e. the normal distribution and the log–normal distribution), variation coefficient, mean value, correlation between parameters on the reliability index of slope is discussed. The study shows that different soil properties have different influence degree on the reliability index with regard to the slope reliability analysis.

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