Home  About us  Contact
 

Gaussian Approximation (gaussian + approximation)

Distribution by Scientific Domains
Mathematics and Statistics40%
Chemistry40%

Selected Abstracts

Performance analysis of optically preamplified DC-coupled burst mode receivers

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 3 2009
T. J. Zuo
Bit error rate and threshold acquisition penalty evaluation is performed for an optically preamplified DC-coupled burst mode receiver using a moment generating function (MGF) description of the signal plus noise. The threshold itself is a random variable and is also described using an appropriate MGF. Chernoff bound (CB), modified Chernoff bound (MCB) and the saddle-point approximation (SPA) techniques make use of the MGF to provide the performance analyses. This represents the first time that these widely used approaches to receiver performance evaluation have been applied to an optically preamplified burst mode receiver and it is shown that they give threshold acquisition penalty results in good agreement with a prior existing approach, whilst having the facility to incorporate arbitrary receiver filtering, receiver thermal noise and non-ideal extinction ratio. A traditional Gaussian approximation (GA) is also calculated and comparison shows that it is clearly less accurate (it exceeds the upper bounds provided by CB and MCB) in the realistic cases examined. It is deduced, in common with the equivalent continuous mode analysis, that the MCB is the most sensible approach. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Gaussian approximation of exponential type orbitals based on B functions

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2009
Didier Pinchon
Abstract This work gives new, highly accurate optimized gaussian series expansions for the B functions used in molecular quantum mechanics. These functions are generally chosen because of their compact Fourier transform, following Shavitt. The inverse Laplace transform in the square root of the variable is used for Gauss quadrature in this work. Two procedures for obtaining accurate gaussian expansions have been compared for the required extended precision arithmetic. The first is based on Gaussian quadratures and the second on direct optimization. Both use the Maple computer algebra system. Numerical results are tabulated and compared with previous work. Special cases are found to agree before pushing the optimization technique further. The optimal gaussian expansions of B functions obtained in this work are available for reference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source]

The resolution function in neutron spin-echo spectroscopy with three-axis spectrometers

JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2003
Klaus Habicht
A resolution function for inelastic neutron spin-echo spectroscopy on a three-axis spectrometer is derived. Inelastic dispersive excitations where the tilted field technique applies are being considered. Using a Gaussian approximation of the transmission function of the three-axis spectrometer and a second-order expansion of the total Larmor phase, the instrumental resolution function of an idealized spin-echo instrument is obtained. Furthermore, the resolution function is extended to include the effects of sample properties, such as mosaicity, spread in lattice spacings and the curvature of the four-dimensional dispersion surface in a line-width measurement. [source]

EXPONENTIAL SMOOTHING AND NON-NEGATIVE DATA

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2009
Muhammad Akram
Summary The most common forecasting methods in business are based on exponential smoothing, and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process. We first demonstrate that prediction distributions from some commonly used state space models may have an infinite variance beyond a certain forecasting horizon. For multiplicative error models that do not have this flaw, we show that sample paths will converge almost surely to zero even when the error distribution is non-Gaussian. We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model. We then explore the implications of our results for inference, and compare the short-term forecasting performance of the various models using data on the weekly sales of over 300 items of costume jewelry. The main findings of the research are that the Gaussian approximation is adequate for estimation and one-step-ahead forecasting. However, as the forecasting horizon increases, the approximate prediction intervals become increasingly problematic. When the model is to be used for simulation purposes, a suitably specified scheme must be employed. [source]

Global Tests for Linkage

BIOMETRICAL JOURNAL, Issue 1 2009
Rachid el Galta
Abstract To test for global linkage along a genome or in a chromosomal region, the maximum over the marker locations of mean alleles shared identical by descent of affected relative pairs, Zmax, can be used. Feingold et al. (1993) derived a Gaussian approximation to the distribution of the Zmax. As an alternative we propose to sum over the observed marker locations along the chromosomal region of interest. Two test statistics can be derived. (1) The likelihood ratio statistic (LR) and (2) the corresponding score statistic. The score statistic appears to be the average mean IBD over all available marker locations. The null distribution of the LR and score tests are asymptotically a 50: 50 mixture of chi-square distributions of null and one degree of freedom and a normal distribution, respectively. We compared empirically the type I error and power of these two new test statistics and Zmax along a chromosome and in a candidate region. Two models were considered, namely (1) one disease locus and (2) two disease loci. The new test statistics appeared to have reasonable type I error. Along the chromosome, for both models we concluded that for very small effect sizes, the score test has slightly more power than the other test statistics. For large effect sizes, the likelihood ratio statistic was comparable to and sometimes performed better than Zmax and both test statistics performed much better than the score test. For candidate regions of about 30 cM, all test statistics were comparable when only one disease-locus existed and the score and likelihood ratio statistics had somewhat better power than Zmax when two disease loci existed (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]