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41.
非傍轴平顶高斯光束M2因子两种定义的比较研究 总被引:1,自引:1,他引:0
基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较.在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关.按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1, 2, 3时,M2因子分别趋于0.913,0.882和0.886.当N→∞时,M2因子取最小值M2min=0.816. 相似文献
42.
43.
Chemical bonding in isolated molecules and crystals of zwitterionic pentacoordinate silicon chelates
The electronic structures of a number of zwitterionic pentacoordinate silicon chelates were investigated using the results of X-ray diffraction studies and quantum-chemical calculatoins by the MPW1PW91/6-311G(d) method. The topological analysis of the electron density distribution function and the study in the framework of the natural bond orbital partitioning scheme showed that the character of chemical bonding in the axial fragments of the molecules under consideration changes from dative to three-center, four-electron as the silicon atom assumes a trigonal-bipyramidal coordination. 相似文献
44.
An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss 总被引:3,自引:0,他引:3
Mohammad Jafari Jozani Nader Nematollahi Khalil Shafie 《Statistics & probability letters》2002,60(4):437-444
A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given. 相似文献
45.
A series of low density polyethylene systems has been studied with respect to structural evolution and short-term dielectric breakdown behaviour. All materials were based upon a single polymer, that is commonly used in high voltage applications, but with different additives. In all three of these systems, multiple melting transitions were observed, as a result of molecular fractionation effects during crystallization. In the virgin polymer, a space-filling banded spherulitic morphology was found to develop at low temperatures (102 °C and below) whereas, at higher temperatures, only a few isolated axialites were observed. Inclusion of the antioxidant resulted in greatly increased nucleation densities, such that, at low temperatures, no evidence of spherulitic organisation remained. At higher temperatures, sheaf-like lamellar aggregates developed, which were much smaller and much more numerous than in the case of the virgin polymer. Further addition of dicumyl peroxide (DCP) resulted in the rapid formation of a crosslinked network at 200 °C. Some crosslinking also occurred at 150 °C, but over a much longer timescale. Where extensive crosslinking occurred prior to crystallization, the resulting gel inhibited structural development, such that only a few small, isolated sheaves were able to form at 102 °C. In view of the principal application area of this material, the breakdown strength of each of the above systems was then measured and the whole data set was analysed statistically. When structural factors were considered alongside the statistics, no clear trends emerged to indicate that either the compositional or morphological variations were reflected in the short-term electrical failure processes. 相似文献
46.
47.
Statistical Inference with Fractional Brownian Motion 总被引:3,自引:1,他引:2
Kukush Alexander Mishura Yulia Valkeila Esko 《Statistical Inference for Stochastic Processes》2005,8(1):71-93
We give a test between two complex hypothesis; namely we test whether a fractional Brownian motion (fBm) has a linear trend against a certain non-linear trend. We study some related questions, like goodness-of-fit test and volatility estimation in these models. 相似文献
48.
The usual tool for modelling bond ratings migration is a discrete, time‐homogeneous Markov chain. Such model assumes that all bonds are homogeneous with respect to their movement behaviour among rating categories and that the movement behaviour does not change over time. However, among recognized sources of heterogeneity in ratings migration is age of a bond (time elapsed since issuance). It has been observed that young bonds have a lower propensity to change ratings, and thus to default, than more seasoned bonds. The aim of this paper is to introduce a continuous, time‐non‐homogeneous model for bond ratings migration, which also incorporates a simple form of population heterogeneity. The specific form of heterogeneity postulated by the proposed model appears to be suitable for modelling the effect of age of a bond on its propensity to change ratings. This model, called a mover–stayer model, is an extension of a Markov chain. This paper derives the maximum likelihood estimators for the parameters of a continuous time mover–stayer model based on a sample of independent continuously monitored histories of the process, and develops the likelihood ratio statistic for discriminating between the Markov chain and the mover–stayer model. The methods are illustrated using a sample of rating histories of young corporate issuers. For these issuers the default probabilities predicted by the Markov chain and mover–stayer models are different. In particular for 1–4 years old bonds the mover–stayer model estimates substantially lower default probabilities from rating C than a Markov chain. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
49.
Dominique Fourdrinier William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2003,55(4):803-816
We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In
3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988,
On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual
estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized
Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly,
that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax
estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes
estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator
of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss.
Research supported by NSF Grant DMS-97-04524. 相似文献
50.
C. H. Hesse 《Statistical Inference for Stochastic Processes》2007,10(1):75-95
In this work the Cauchy problem for the one-dimensional heat equation is considered. In contrast to existing literature it
is assumed that the initial state f is unknown and that information regarding f is obtained by some process of measurement. To enhance realism, both measurement errors and missing data are allowed for.
Under assumptions on f in the Fourier-domain first an approximation to f is derived from the data by means of a novel uncertainty principle. Then, it is studied how this perturbation in the initial
state propagates with time.
相似文献