The Asymptotic Behavior of INAR (p) Models

An integer-valued autoregressive model with random time delay under random environment is presented. The geometric ergodicity of the iterative sequence determined by this new model is discussed. Moreover, sufficient conditions for stationarity and β-mixing property with exponential decay for the INAR model with random time delay under random environment are developed.     

Testing fit for the grouped exponential distribution

Grouped data can often arise due to the lack of resolution of the measurement instruments; they also arise when data are deliberately rounded to a certain accuracy and are presented, say, in the form of a histogram. The author uses statistics of the Cramér‐von Mises type to test for the exponential distribution when data are grouped.     

Slope estimation of covariates that influence renal outcome following renal transplant adjusting for informative right censoring

A new statistical model is proposed to estimate population and individual slopes that are adjusted for covariates and informative right censoring. Individual slopes are assumed to have a mean that depends on the population slope for the covariates. The number of observations for each individual is modeled as a truncated discrete distribution with mean dependent on the individual subjects’ slopes. Our simulation study results indicated that the associated bias and mean squared errors for the proposed model were comparable to those associated with the model that only adjusts for informative right censoring. The proposed model was illustrated using renal transplant dataset to estimate population slopes for covariates that could impact the outcome of renal function following renal transplantation.     

Ergodicity of generalized Ait-Sahalia-type interest rate model

In this paper, we consider sufficient conditions for the stationary distribution of generalized Ait-Sahalia-type interest rate model. We show that if r ? 2ρ ? 1, then the generalized Ait-Sahalia interest rate model has a unique stationary distribution and if r < 2ρ ? 1, then the generalized Ait-Sahalia interest rate model is recurrent relative to the domain (0, ?), for any ? > 0. Besides, some recursion formulas for the stationary distribution are presented. Finally, some numerical simulations are used to illustrate our results.     

四阶常微分算子特征值的重数相等

借助解析重数和几何重数的基本定义及边界条件的几何结构,证明了自伴的四阶常微分算子特征值的解析重数与几何重数是相等的,该结论是对常型Sturm-Liouville问题相关结果的推广.     

卡尔维诺的叙事奇观

本文以几何叙事和晶体形象两部分 ,对意大利作家卡尔维诺的主要作品进行解析 ,主要从后现代主义的叙事角度展现大师的创作理念和叙事奇观     

基于对偶犹豫模糊几何Heronian平均算子的多属性决策方法及其应用

针对需要同时考虑变量隶属度、非隶属度以及关联性的融合问题,本文将对偶犹豫模糊集与Heronian平均算子相结合,定义了对偶犹豫模糊几何Heronian平均算子和对偶犹豫模糊几何加权Heronian平均算子,讨论了新算子的一些优良特性,包括幂等性、置换不变性、有界性、单调性等性质,并针对属性值为对偶犹豫模糊语言信息关联系的多属性决策问题,建立了基于对偶犹豫模糊几何加权Heronian平均算子的多属性决策模型,基于所定义的算子和建立的数学模型,提出了一种新的基于对偶犹豫模糊Heronian平均算子的多属性决策方法。最后,通过多属性决策算例验证了方法的有效性和可行性。     

Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes

Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation models for failure based on the geometric Brownian motion or gamma process. It is shown that in most cases, our models for failure can be approximated closely by accelerated test versions of Birnbaum–Saunders and inverse Gaussian distributions. Estimation of model parameters and a model selection procedure are discussed, and two illustrative examples using real data for carbon-film resistors and fatigue crack size are presented.     

The Probability Distribution for the Number of Successes in Independent Trials

The number of successes S in n independent trials is one of the classic distributions in statistics. When the probability of success p is constant, S has the binomial distribution with parameters n and p. Distributional properties of S in the homogeneous case are well known, but they are considerably harder to establish when p varies. A brief historical review is undertaken to highlight some of the more important results obtained over the past 50 years. In spite of the progress made, there are still some important open problems concerning stochastic comparisons for S that deserve to be solved!     

Geometric Ergodicity and Moment Conditions for a Seasonal GARCH Model with Periodic Coefficients

A seasonal GARCH process with periodic coefficients is considered and conditions for periodic stationarity, geometric ergodicity, β-mixing property with exponential decay rate, and existence of higher-order moments are obtained.