An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

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.     

On the identifiability of multivariate survival distribution functions

Let (T₁, T₂) be a non-negative random vector which is subjected to censoring random intervals [X₁, Y₁] and [X₂, Y₂]. The censoring mechanism is such that the available informations on T₁ and T₂ are expressed by a pair of random vectors W=(W₁, W₂) and δ=(δ₁, δ₂), where W_i=max(min(Y_i, T_i), X_i) and In this paper we will show that under some mild conditions the joint survival function of T₁ and T₂ can be expressed uniquely as functional of observable joint survival functions. Our results extend recent works on the randomly right censored bivariate data case and on the univariate problem with double censoring to the bivariate data with double censoring.     

Multivariate dynamic information

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.     

Surface morphology of Ge‐modified 3C‐SiC/Si films

The influence of Ge deposition prior to carbon interaction with 3° off‐axis Si(111) substrates on the structural and morphological properties of the formed silicon carbide (SiC) layer is studied. In situ reflection high‐energy electron diffraction (RHEED) and X‐ray diffraction (XRD) revealed the formation of the cubic silicon carbide (3C‐SiC) modification. In situ spectroscopic ellipsometry measurements revealed a decreasing 3C‐SiC thickness with increasing Ge predeposition. Atomic force microscopy (AFM) studies revealed that the surface overlayer morphology is mainly formed by periodic step arrangements whose relevant geometric parameters, i.e. lateral separation, height and terrace width, depend on the Ge content. Besides the changes of the step morphology, the surface roughness and the grain size and the strain of the formed 3C‐SiC decreases with increasing germanium precoverage. Copyright © 2008 John Wiley & Sons, Ltd.     

SiC polytypes process affected by Ge predeposition on Si(111) substrates

Structural and optical measurements were performed on silicon carbide (SiC) samples containing several polytypes. The SiC samples investigated were grown on (111) Si substrates by solid source molecular beam epitaxy (SSMBE). Several quantities of Ge were predeposited before the growth procedure. The influence of Ge on the SiC polytypes formation was studied by X-Ray, FTIR and μ-Raman characterizations methods. The spectra of the samples with less than one Ge monolayer exhibit a mixture of 2H, 15R and 3C–SiC polytypes. This mixture is due to the mismatch between the heterostructure layers. We propose that the Ge predeposition in the heterostructure can be used to stabilize and unify the polytypes formation.     

Onk-order harmonic new better than used in expectation distributions

Summary Definitions ofk-HNBUE andK-HNWUE are introduced and the relationship with other class of life distributions is studied. Various closure properties ofk-HNBUE (k-HNWUE) are proved. Finally bounds on the moments and survival function ofk-HNBUE (k-HNWUE) are given. This research was supported by the ONR Grant N00014-78-C-0655.     

Application of the frontal algorithm in the collocation method

The author reports on a numerical experimentation with the collocation finite element procedure using Hermite basis functions and the frontal elimination technique to solve some large-scale problems where up to 1000 linear equations are involved. Several test cases, including some applications to engineering problems, are presented. The implementation of the frontal technique applied to collocation is discussed to some extent.