Forecasting Spanish Natural Life Expectancy

Knowledge of trends in life expectancy is of major importance for policy planning. It is also a key indicator for assessing future development of life insurance products, substantiality of existing retirement schemes, and long-term care for the elderly. This article examines the feasibility of decomposing age-gender-specific accidental and natural mortality rates. We study this decomposition by using the Lee and Carter model. In particular, we fit the Poisson log-bilinear version of this model proposed by Wilmoth and Brouhns et al. to historical (1975-1998) Spanish mortality rates. In addition, by using the model introduced by Wilmoth and Valkonen we analyze mortality-gender differentials for accidental and natural rates. We present aggregated life expectancy forecasts compared with those constructed using nondecomposed mortality rates.     

Are football referees really biased and inconsistent?: evidence on the incidence of disciplinary sanction in the English Premier League

Summary.  The paper presents a statistical analysis of patterns in the incidence of disciplinary sanction (yellow and red cards) that were taken against players in the English Premier League over the period 1996–2003. Several questions concerning sources of inconsistency and bias in refereeing standards are examined. Evidence is found to support a time consistency hypothesis, that the average incidence of disciplinary sanction is predominantly stable over time. However, a refereeing consistency hypothesis, that the incidence of disciplinary sanction does not vary between referees, is rejected. The tendency for away teams to incur more disciplinary points than home teams cannot be attributed to the home advantage effect on match results and appears to be due to a refereeing bias favouring the home team.     

经典一阶逻辑的希尔伯特型系统

系统Z是文[7]构造的经典命题逻辑系统,这一系统的初始联结词是一类广义的谢夫竖函数,并且采用括号记法。作者在系统Z中加入存在量词,把存在量词和广义谢夫竖函数统一作括号记法,并且把系统Z的规则作相应的处理,最后证明了所得系统Z'的完全性。     

与四阶矩阵特征问题相关的约束流与完全可积系统

主要讨论与四阶矩阵特征值问题相联系的孤子方程及其Lax上,利用位势函数与特征函数之间的Bargmann约束,将四阶特征值问题及相应的伴随特征值问题非线性化,获得新的有限维Hamilton系统,并应用r-矩阵理论证明了新的有限维Hamilton系统在Liouville意义下的完全可积性。最后借助于在Liouville意义下完全可积Hamilton系统的对合解得到孤子方程族解的对合表示。     

Robust inference for bivariate point processes

In the analysis of recurrent events where the primary interest lies in studying covariate effects on the expected number of events occurring over a period of time, it is appealing to base models on the cumulative mean function (CMF) of the processes (Lawless & Nadeau 1995). In many chronic diseases, however, more than one type of event is manifested. Here we develop a robust inference procedure for joint regression models for the CMFs arising from a bivariate point process. Consistent parameter estimates with robust variance estimates are obtained via unbiased estimating functions for the CMFs. In most situations, the covariance structure of the bivariate point processes is difficult to specify correctly, but when it is known, an optimal estimating function for the CMFs can be obtained. As a convenient model for more general settings, we suggest the use of the estimating functions arising from bivariate mixed Poisson processes. Simulation studies demonstrate that the estimators based on this working model are practically unbiased with robust variance estimates. Furthermore, hypothesis tests may be based on the generalized Wald or generalized score tests. Data from a trial of patients with bronchial asthma are analyzed to illustrate the estimation and inference procedures.     

Statistical models of near-accident event and pedestrian behavior at non-signalized intersections

This paper proposes an innovative framework of modeling the statistical properties of the near-accident event and pedestrian behavior at non-signalized intersections based on Poisson process and logistic regression. The first contribution of this study is that the predictive intensity model of the near-accident event is established by regarding the near-accident event as a Poisson process on space of the vehicle velocity, distance to the intersection and lateral distance to the pedestrian at the time when pedestrian appears. Besides, logistic regression is used to build the model which can predict the probability of pedestrian behavior. The two proposed models are validated in a generative simulation. The simulated pedestrian behavior data is generated by the proposed models and compared with the real data. The real data set is from the drive recorder data base of Smart Mobility Research Center (SMRC) at Tokyo University of Agriculture and Technology. Accident and near-accident data has been collected in the city streets with an image-captured drive recorder mounted on a taxi since 2006. The findings in this study are expected to be useful for constructions of traffic simulators or safety control design which considers the pedestrian-vehicle interaction.     

The non-central negative binomial distribution: Further properties and applications

Abstract

The non-central negative binomial distribution is both a mixed and compound Poisson distribution with applications in photon and neural counting, statistical optics, astronomy and a stochastic reversible counter system. In this paper various important probabilistic properties of the non-central negative binomial distribution in practical applications like log-concavity, discrete self-decomposability, unimodality, asymptotic behavior and tail length of the probability distribution have been derived. The construction as a mixed Poisson process by specifying a joint distribution for the inter-arrival times and its application is illustrated by a fit to real life data set.     

春秋时代华夏集团每年受围次数的模型分析报告

本文以《春秋》统计资料为样本 ,建立并检验了描写春秋时代华夏集团受围情况的数学模型 ,依据模型探讨了围城战频繁发生的主因 ,推论了“历史的复原”和“史学的积累”的可能性     

Approximating the Conway–Maxwell–Poisson distribution normalization constant

By adding a second parameter, Conway and Maxwell created a new distribution for situations where data deviate from the standard Poisson distribution. This new distribution contains a normalization constant expressed as an infinite sum whose summation has no known closed-form expression. Shmueli et al. produced an approximation for this sum but proved that it was valid only for integer values of the second parameter, although they conjectured it was also valid for non-integers. Here we prove their conjecture to be true and discuss for what range of parameters the approximation can be accurately applied.