scholarly journals Tsallis Entropy of Uncertain Random Variables and Its Application

2021 ◽  
Author(s):  
Zhenhua He ◽  
Hamed Ahmadzade ◽  
Kamran Rezaei ◽  
Hassan Rezaei ◽  
Habib Naderi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Search Algorithm ◽  
Random Variables ◽  
Random Variable ◽  
Tsallis Entropy ◽  
Uncertain Random Variable ◽  
Chance Theory ◽  
Entropy Measures ◽  
Selection Of

Abstract Tsallis entropy ia a flexible extension of Shanon (logarithm) entropy. Since, entropy measures indeterminacy of an uncertain random variable, this paper proposes the concept of partial Tsallis entropy for uncertain random variables as a flexible devise in chance theory. An approach for calculating partial Tsallis entropy for uncertain random variables, based on Monte-Carlo simulation, is provided. As an application in finance, partial Tsallis entropy is invoked to optimize portfolio selection of uncertain random returns via crow search algorithm.

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.

scholarly journals Improving the Asmussen–Kroese-Type Simulation Estimators

2012 ◽  
Vol 49 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Samim Ghamami ◽  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Nonnegative Integer ◽  
Rare Event ◽  
Random Variables ◽  
Random Variable ◽  
Heavy Tailed ◽  
Independent Identically Distributed

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

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.

Exact cash-account deflator for the G2++ model

2020 ◽  
Vol 07 (01) ◽  
pp. 2050009
Author(s):  
Francesco Strati ◽  
Luca G. Trussoni
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Insurance Industry ◽  
Random Variable ◽  
Time Span ◽  
Discrete Random Variable ◽  
Variable Formula ◽  
Monte Carlo Simulation Technique ◽  
Insurance Contracts ◽  
Embedded Options

In this paper, we shall propose a Monte Carlo simulation technique applied to a G2++ model: even when the number of simulated paths is small, our technique allows to find a precise simulated deflator. In particular, we shall study the transition law of the discrete random variable :[Formula: see text] in the time span [Formula: see text] conditional on the observation at time [Formula: see text], and we apply it in a recursive way to build the different paths of the simulation. We shall apply the proposed technique to the insurance industry, and in particular to the issue of pricing insurance contracts with embedded options and guarantees.

scholarly journals Uncertainty Analysis of Greenhouse Gas (GHG) Emissions Simulated by the Parametric Monte Carlo Simulation and Nonparametric Bootstrap Method

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4965
Author(s):  
Kun Mo Lee ◽  
Min Hyeok Lee ◽  
Jong Seok Lee ◽  
Joo Young Lee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Emission Factor ◽  
Bootstrap Method ◽  
Ghg Emissions ◽  
Parametric Bootstrap ◽  
Random Variable ◽  
Ghg Emission ◽  
Nonparametric Bootstrap ◽  
Mcs Method

Uncertainty of greenhouse gas (GHG) emissions was analyzed using the parametric Monte Carlo simulation (MCS) method and the non-parametric bootstrap method. There was a certain number of observations required of a dataset before GHG emissions reached an asymptotic value. Treating a coefficient (i.e., GHG emission factor) as a random variable did not alter the mean; however, it yielded higher uncertainty of GHG emissions compared to the case when treating a coefficient constant. The non-parametric bootstrap method reduces the variance of GHG. A mathematical model for estimating GHG emissions should treat the GHG emission factor as a random variable. When the estimated probability density function (PDF) of the original dataset is incorrect, the nonparametric bootstrap method, not the parametric MCS method, should be the method of choice for the uncertainty analysis of GHG emissions.

Markov Chain Monte Carlo simulation of the distribution of some perpetuities

1999 ◽  
Vol 31 (01) ◽  
pp. 112-134 ◽  
Author(s):  
Jostein Paulsen ◽  
Arne Hove
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Lévy Process ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Levy Process ◽  
Present Value ◽  
Strong Markov

We study the present value Z ∞ = ∫0 ∞ e-X t- dY t where (X,Y) is an integrable Lévy process. This random variable appears in various applications, and several examples are known where the distribution of Z ∞ is calculated explicitly. Here sufficient conditions for Z ∞ to exist are given, and the possibility of finding the distribution of Z ∞ by Markov chain Monte Carlo simulation is investigated in detail. Then the same ideas are applied to the present value Z - ∞ = ∫0 ∞ exp{-∫0 t R s ds}dY t where Y is an integrable Lévy process and R is an ergodic strong Markov process. Numerical examples are given in both cases to show the efficiency of the Monte Carlo methods.

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