Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

One-Dimensional Poisson Growth Models With Random and Asymmetric Growth

Suppose there is a Poisson process of points X _i on the line. Starting at time zero, a grain begins to grow from each point X _i , growing at rate A _i to the left and rate B _i to the right, with the pairs (A _i , B _i ) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A _i +B _i , and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A _i , B _i ) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A _i =B _i =1. Simulation results are given to illustrate the various theorems.     

Ce偶-偶同位素低激发态性质的IBM2描述

通过考虑同类核子相干对间的四极相互作用，在IBM2中对Ce偶－偶同位素^128Ce-^138Ce的低激发态能谱和E2跃迁几率及分支比进行了理论分析，计算结果有效地改善了IBM中这些核的γ带能谱的Staggering现象描述，与实验观察到的低激发态结果基本一致。     

Duane模型在斯特林制冷机研制过程中的应用

介绍一种实用的可靠性增长模型杜安 (Duane)模型 ,并探讨如何运用该模型来分析、指导斯特林制冷机的可靠性增长试验 ,包括试验前的准备、试验数据的处理、曲线的绘制 ,以及如何对增长过程进行估计和监测     

Researches of DC—Problem Under the Model S in which the Numbers of Defective Coins are not Fixed

In this paper,we research general Defective Cion Problem under the model S,i.e,the number d of Defective cions is not fixed. For d=O,1,or 2. we get some good results.     

Urn模型的B网及其应用

Urn模型的离散概率分布被用于构造逼近格式,具有Bernstein多项式的许多特性。本文用B网技术对Urn模型概率分布给出新的解释,指出了Urn模型B网的诸多性质,导出分布函数曲线的导数公式,构造了Urn分布的对偶基及与此相关的拟插值算子。     

Critical behavior in a model of correlated percolation

We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and – clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.     

A Simple Chaotic Circuit with Impulsive Switch Depending on Time and State

This paper presents a simple chaotic circuit consisting of two capacitors, one linear two-port VCCS and one time-state-controlled impulsive switch. The impulsive switch causes rich chaotic and periodic behavior. The circuit dynamics can be simplified into a one-dimensional return map that is piecewise linear and piecewise monotone. Using the return map, we clarify parameter conditions for existence of chaotic and periodic attractors and coexistence state of attractors.     

灰色Verhulst模型的样条插值函数的残差修正

本用样条函数对灰色Verhulst模型的残差序列进行插值拟合，然后作用于二阶线性微分方程，并以此修正原模型，得到一种新的预测模型的数值解，提高了拟合的精确度。