The exponential Poisson logarithmic distribution

Abstract

In this article, we proposed a new three parameter lifetime distribution motivated mainly by lifetime issues, which generalizes the Exponential Poisson distribution proposed by Cancho et al. (2011) Cancho, V.G., Louzada-Neto, F., Barriga, G.D. (2011). The poisson-exponential lifetime distribution. Computat. Statist. Data Anal. 55:677–686.[Crossref], [Web of Science ®] , [Google Scholar]. We derive various standard mathematical properties of the proposed model including a formal proof of its probability density function and hazard rate function. The inference via the maximum likelihood approach is discussed. The performance of the maximum likelihood estimators, the likelihood ratio test and its power are studied by simulation. Finally, the proposed model is fitted to two real data sets and it is compared with several models.     

Stochastic EM algorithm of a finite mixture model from hurdle Poisson distribution with missing responses

ABSTRACT

In this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic EM algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology.     

Exponentially weighted moving average charts for correlated multivariate Poisson processes

In this article, we study exponentially weighted moving average (EWMA) control schemes to monitor the multivariate Poisson distribution with a general covariance structure, so that the practitioner can simultaneously monitor multiple correlated attribute processes more effectively. The statistical performance of the charts is assessed in terms of the run length properties and compared against other mainstream attribute control schemes. The application of the proposed methods to real-life and simulated datasets is demonstrated.     

Robust Poisson likelihood estimation for frailty Cox models: A simulation study

Frailty models can be fit as mixed-effects Poisson models after transforming time-to-event data to the Poisson model framework. We assess, through simulations, the robustness of Poisson likelihood estimation for Cox proportional hazards models with log-normal frailties under misspecified frailty distribution. The log-gamma and Laplace distributions were used as true distributions for frailties on a natural log scale. Factors such as the magnitude of heterogeneity, censoring rate, number and sizes of groups were explored. In the simulations, the Poisson modeling approach that assumes log-normally distributed frailties provided accurate estimates of within- and between-group fixed effects even under a misspecified frailty distribution. Non-robust estimation of variance components was observed in the situations of substantial heterogeneity, large event rates, or high data dimensions.     

广西农业剩余劳动力转移状况研究

广西要想在西部率先全面建成小康社会。必须解决好农业剩余劳动力的转移问题。本文使用抽样法测算广西2008年农业剩余劳动力总数,并按照劳动力转移去向进行统计分析,揭示转移中存在的突出性问题和提出对策建议。     

对我国2010年人口普查事后调查工作的若干建议

人口普查不可能100％计数每一个人。世界上许多国家都在人口普查后组织事后调查,使用双系统估计量另行求得一个全国人口真实数的估计数,并以此为标准估计人口普查的净遗漏率。我国历次人口普查后都进行了事后调查,其主要缺陷是未对抽取的样本事后分层,未估计“全国真实的人口数”。建议我国2010年事后调查方案在克服这两个缺陷的基础上科学确定全国的样本总量。实行两步抽样等。     

Application of the Hyper‐Poisson Generalized Linear Model for Analyzing Motor Vehicle Crashes

The hyper‐Poisson distribution can handle both over‐ and underdispersion, and its generalized linear model formulation allows the dispersion of the distribution to be observation‐specific and dependent on model covariates. This study's objective is to examine the potential applicability of a newly proposed generalized linear model framework for the hyper‐Poisson distribution in analyzing motor vehicle crash count data. The hyper‐Poisson generalized linear model was first fitted to intersection crash data from Toronto, characterized by overdispersion, and then to crash data from railway‐highway crossings in Korea, characterized by underdispersion. The results of this study are promising. When fitted to the Toronto data set, the goodness‐of‐fit measures indicated that the hyper‐Poisson model with a variable dispersion parameter provided a statistical fit as good as the traditional negative binomial model. The hyper‐Poisson model was also successful in handling the underdispersed data from Korea; the model performed as well as the gamma probability model and the Conway‐Maxwell‐Poisson model previously developed for the same data set. The advantages of the hyper‐Poisson model studied in this article are noteworthy. Unlike the negative binomial model, which has difficulties in handling underdispersed data, the hyper‐Poisson model can handle both over‐ and underdispersed crash data. Although not a major issue for the Conway‐Maxwell‐Poisson model, the effect of each variable on the expected mean of crashes is easily interpretable in the case of this new model.     

CreditRisk+模型采用Poisson分布所产生的经济资本计量误差分析

本文对CreditRisk+模型采用Poisson分布近似债务人违约事件分布这一关键步骤进行系统研究。首先分析了Poisson分布在CreditRisk+模型中的作用,并从理论上证明了采用Poisson分布作为债务人违约事件分布的近似,会导致CreditRisk+模型计算出来的经济资本高估贷款组合的实际风险水平;然后以债务人违约事件服从两点分布并采用蒙特卡罗模拟计算出来的经济资本为参照值,对债务人违约概率的大小与这一近似所引起的经济资本计量误差率进行了敏感性试验,发现为将这一近似所引起的误差率控制在10%的范围内,债务人违约概率的取值不应超过0.2。     

Algorithms Section: Introduction

Electronic Access to Algorithms
Applied Statistics algorithms are available on Statlib at Carnegie Mellon University and on the UK mirror of Statlib at the University of Kent. They may be accessed either via anonymous file transfer protocol (FTP) or by WWW mosaic.