Transient Analysis of Large Markov Models with Absorbing States Using Regenerative Randomization

ABSTRACT

In this article, we develop a new method, called regenerative randomization, for the transient analysis of continuous time Markov models with absorbing states. The method has the same good properties as standard randomization: numerical stability, well-controlled computation error, and ability to specify the computation error in advance. The method has a benign behavior for large t and is significantly less costly than standard randomization for large enough models and large enough t. For a class of models, class C, including typical failure/repair reliability models with exponential failure and repair time distributions and repair in every state with failed components, stronger theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. A large example belonging to that class is used to illustrate the performance of the method and to show that it can indeed be much faster than standard randomization.     

A class of bivariate regression models for discrete and/or continuous responses

ABSTRACT

A general class of models for discrete and/or continuous responses is proposed in which joint distributions are constructed via the conditional approach. It is assumed that the distributions of one response and of the other response given the first one belong to exponential family of distributions. Furthermore, the marginal means are related to the covariates by link functions and a dependency structure between the responses is inserted into the model. Estimation methods, diagnostic analysis and a simulation study considering a Bernoulli-exponential model, a particular case of the class, are presented. Finally, this model is used in a real data set.     

A new estimator of entropy

Vasicek (1976) proposed an estimator of entropy based on spacings. A new estimator of entropy is proposed. This new estimator is based on local linear regression. Comparisons between this new estimator and Vasicek's estimator are made. The mean square error (MSE) of the new estimator is consistently smaller than the MSE of Vasicek's estimator.     

Waiting time to exhaust lottery numbers

Questions related to lotteries are usually of interest to the public since people think there is a magic formula which will help them to win lottery draws. This note shows how to compute the expected waiting time to observe specific numbers in a sequence of lottery draws and show that surprising facts are expected to occur.     

Accuracy of approximate progressively censored reliability sampling plans for exponential models

Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter case. Some additional advantages are also pointed out.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.     

Exploring the characteristics of rotating electric machines with factor analysis

Applications of multivariate statistics in engineering are hard to find, apart from those in quality control. However, we think that further insight into some technological cases may be gained by using adequate multivariate analysis tools. In this paper, we propose a review of the key parameters of rotating electric machines with factor analysis. This statistical technique allows not only the reduction of the dimension of the case we are analysing, but also reveals subtle relationships between the variables under study. We show an application of this methodology by studying the interrelations between the key variables in an electric machine, in this case the squirrel-cage induction motor. Through a step-by-step presentation of the case study, we deal with some of the topics an applied researcher may face, such as the rotation of the original factors, the extraction of higher-order factors and the development of the exploratory model. As a result, we present a worthwhile framework to both confirm our previous knowledge and capture unexplored facts. Moreover, it may provide a new approach to describing and understanding the design, performance and operating characteristics of these machines.     

论新闻语言的主观化

新闻报道有其客观性原则,但整个新闻传播活动却充满了主观性。主观性体现在很多方面,新闻语言的主观化就是最重要的方面之一。从总体上看,新闻事实的外化过程就是实现语言的主观化过程;从手段方面看,焦点标记词的使用、焦点位置的安排、主观评价意图的外显等都在实现新闻语言主观化上发挥重要作用。     

A Multivariate Indicator to Compute Middle Class Population

Social Indicators Research - Monitoring progress towards the Sustainable Development Goals by 2030 requires the global community to disaggregate targets along socio-economic lines, but little has...     

Urban vegetation cover correlates with environmental variables in a desert city: insights of mitigation measures to climate change

Urban Ecosystems - Green cover and air quality are important components of life quality and human ecology in arid lands. In the Sonoran Desert of Mexico, Hermosillo is the largest city with a...