Abstract: Edgeworth Approximation, Bootstrap and Monte Carlo Simulations have a considerable impact on the achieving certain results related to different problems taken into study. In our paper, we have treated a financial case related to the effect that have the components of a Cash-Flow of one of the most successful businesses in the world, as the financial activity, operational activity and investing activity to the cash and cash equivalents at the end of the three-months period. To have a better view of this case we have created a Vector Autoregression model, and after that we have generated the impulse responses in the terms of Asymptotic Analysis (Edgeworth Approximation), Monte Carlo Simulations and Residual Bootstrap based on the standard errors of every series created. The generated results consisted of the common tendencies for the three methods applied, that consequently verified the advantage of the three methods in the optimization of the model that contains many variants.
Abstract: This paper is to compare the parameter estimation of
the mean in normal distribution by Maximum Likelihood (ML),
Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML
estimator is estimated by the average of data, the Bayes method is
considered from the prior distribution to estimate Bayes estimator,
and MCMC estimator is approximated by Gibbs sampling from
posterior distribution. These methods are also to estimate a parameter
then the hypothesis testing is used to check a robustness of the
estimators. Data are simulated from normal distribution with the true
parameter of mean 2, and variance 4, 9, and 16 when the sample
sizes is set as 10, 20, 30, and 50. From the results, it can be seen
that the estimation of MLE, and MCMC are perceivably different
from the true parameter when the sample size is 10 and 20 with
variance 16. Furthermore, the Bayes estimator is estimated from the
prior distribution when mean is 1, and variance is 12 which showed
the significant difference in mean with variance 9 at the sample size
10 and 20.
Abstract: Lattice Monte Carlo methods are an excellent
choice for the simulation of non-linear thermal diffusion
problems. In this paper, and for the first time, Lattice Monte
Carlo analysis is performed on thermal diffusion combined
with convective heat transfer. Laminar flow of water modeled
as an incompressible fluid inside a copper pipe with a constant
surface temperature is considered. For the simulation of
thermal conduction, the temperature dependence of the
thermal conductivity of the water is accounted for. Using the
novel Lattice Monte Carlo approach, temperature distributions
and energy fluxes are obtained.
Abstract: A code has been developed in Mathematica using
Direct Simulation Monte Carlo (DSMC) technique. The code was
tested for 2-D air flow around a circular cylinder. Same geometry
and flow properties were used in FLUENT 6.2 for comparison. The
results obtained from Mathematica simulation indicated significant
agreement with FLUENT calculations, hence providing insight into
particle nature of fluid flows.