428,327 research outputs found
Studies on properties and estimation problems for modified extension of exponential distribution
The present paper considers modified extension of the exponential
distribution with three parameters. We study the main properties of this new
distribution, with special emphasis on its median, mode and moments function
and some characteristics related to reliability studies. For Modified-
extension exponential distribution (MEXED) we have obtained the Bayes
Estimators of scale and shape parameters using Lindley's approximation
(L-approximation) under squared error loss function. But, through this
approximation technique it is not possible to compute the interval estimates of
the parameters. Therefore, we also propose Gibbs sampling method to generate
sample from the posterior distribution. On the basis of generated posterior
sample we computed the Bayes estimates of the unknown parameters and
constructed 95 % highest posterior density credible intervals. A Monte Carlo
simulation study is carried out to compare the performance of Bayes estimators
with the corresponding classical estimators in terms of their simulated risk. A
real data set has been considered for illustrative purpose of the study.Comment: 22,
Direct search for the optimum of a simulated process continuing noise
The objective of this work was to study the optimization of a function whose measurement contains error or noise. A search method developed for noise free systems was applied to a noisy function using minimum variance estimators to improve the accuracy of the functional values. The results of the new search method are compared to those of a modified stochastic approximation method which has good convergence on noisy systems.
At moderate noise levels (Ï â€ 0.5), the new method appears to converge faster than the best method reported for the modified stochastic approximation although at higher noise levels (Ï > 0.5), this advanÂtage seems to be lost
Rational spectral methods for PDEs involving fractional Laplacian in unbounded domains
Many PDEs involving fractional Laplacian are naturally set in unbounded
domains with underlying solutions decay very slowly, subject to certain power
laws. Their numerical solutions are under-explored. This paper aims at
developing accurate spectral methods using rational basis (or modified mapped
Gegenbauer functions) for such models in unbounded domains. The main building
block of the spectral algorithms is the explicit representations for the
Fourier transform and fractional Laplacian of the rational basis, derived from
some useful integral identites related to modified Bessel functions. With these
at our disposal, we can construct rational spectral-Galerkin and direct
collocation schemes by pre-computing the associated fractional differentiation
matrices. We obtain optimal error estimates of rational spectral approximation
in the fractional Sobolev spaces, and analyze the optimal convergence of the
proposed Galerkin scheme. We also provide ample numerical results to show that
the rational method outperforms the Hermite function approach
Rational approximations in Analytic QCD
We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an
infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes
function and, as a consequence, the paradiagonal Pade approximants converge to
the coupling in the entire -plane except on the time-like semiaxis below
the cut. The equivalence between the narrow width approximation of the
discontinuity function of the coupling, on the one hand, and this Pade
(rational) approximation of the coupling, on the other hand, is shown. We
approximate the analytic analogs of the higher powers of mMA coupling by
rational functions in such a way that the singularity region is respected by
the approximants.Several comparisons, for real and complex arguments ,
between the exact and approximate expressions are made and the speed of
convergence is discussed. Motivated by the success of these approximants, an
improvement of the mMA coupling is suggested, and possible uses in the
reproduction of experimental data are discussed.Comment: 12 pages,9 figures (6 double figures); figs.6-8 corrected due to a
programming error; analysis extended to two IR cutoffs; Introduction
rewritten; to appear in J.Phys.
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