Asymptotic Comparison of Method of Moments Estimators and Maximum Likelihood Estimators of Parameters in Zero-Inflated Poisson Model

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.

A Note on the Characterization of Zero-Inflated Poisson Model

Zero-Inflated Poisson model has found a wide variety of applications in recent years in statistical analyses of count data, especially in count regression models. Zero-Inflated Poisson model is characterized in this paper through a linear differential equation satisfied by its probability generating function [1] [2].

Modelling tree mortality across diameter classes using mixedeffects zero-inflated models

The mortality of trees across diameter class model is a useful tool for predicting changes in stand structure.Mortality data commonly contain a large fraction of zeros and general discrete models thus show more errors.Based on the traditional Poisson model and the negative binomial model,different forms of zero-inflated and hurdle models were applied to spruce-fir mixed forests data to simulate the number of dead trees.By comparing the residuals and Vuong test statistics,the zero-inflated negative binomial model performed best.A random effect was added to improve the model accuracy;however,the mixed-effects zero-inflated model did not show increased advantages.According to the model principle,the zeroinflated negative binomial model was the most suitable,indicating that the"0"events in this study,mainly from the sample"0",i.e.,the zero mortality data,are largely due to the limitations of the experimental design and sample selection.These results also show that the number of dead trees in the diameter class is positively correlated with the number of trees in that class and the mean stand diameter,and inversely related to class size,and slope and aspect of the site.

The Need for Structural Adjustment: Was It Essential for African Countries over the Decade of the 80’s? An Econometric Analysis Using Count Data Models

Several economists agree to say that the need for adjustment was essential for African countries over the decade of the 80’s. The econometric analysis of a sample of 28 sub-Saharan African countries, from variables regarded as “representatives” for the adjustment objectives, proves that this assertion cannot be completely rejected.

Road Crash Prediction Models: Different Statistical Modeling Approaches

Road crash prediction models are very useful tools in highway safety, given their potential for determining both the crash frequency occurrence and the degree severity of crashes. Crash frequency refers to the prediction of the number of crashes that would occur on a specific road segment or intersection in a time period, while crash severity models generally explore the relationship between crash severity injury and the contributing factors such as driver behavior, vehicle characteristics, roadway geometry, and road-environment conditions. Effective interventions to reduce crash toll include design of safer infrastructure and incorporation of road safety features into land-use and transportation planning;improvement of vehicle safety features;improvement of post-crash care for victims of road crashes;and improvement of driver behavior, such as setting and enforcing laws relating to key risk factors, and raising public awareness. Despite the great efforts that transportation agencies put into preventive measures, the annual number of traffic crashes has not yet significantly decreased. For in-stance, 35,092 traffic fatalities were recorded in the US in 2015, an increase of 7.2% as compared to the previous year. With such a trend, this paper presents an overview of road crash prediction models used by transportation agencies and researchers to gain a better understanding of the techniques used in predicting road accidents and the risk factors that contribute to crash occurrence.

复合Poisson-Geometric过程风险模型推广

针对经典风险模型中Poisson过程均值必须等于方差这一局限,将其推广到复合Poisson-Geometric过程,并将保费收取次数看作是一个Poisson过程,且每次收到的保费看作是一个随机变量且服从指数分布,得到了对古典风险模型的一个推广.解释了做出这种推广的实际意义,经过推算,得到了调节系数以及破产概率的表达式,进而得到了模型对应的Lundeberg不等式.

稀疏过程在双广义复合poisson风险模型中的应用

为了描述了稀疏过程在双广义复合poisson风险模型中的应用,对经典的复合poisson风险模型进行了改进,给出了关于调节系数所满足的方程,进而得到破产概率的一般表达式和它的一个上界。

An Exceptional Generalization of the Poisson Distribution

A new two-parameter count distribution is derived starting with probabilistic arguments around the gamma function and the digamma function. This model is a generalization of the Poisson model with a noteworthy assortment of qualities. For example, the mean is the main model parameter;any possible non-trivial variance or zero probability can be attained by changing the other model parameter;and all distributions are visually natural-shaped. Thus, exact modeling to any degree of over/under-dispersion or zero-inflation/deflation is possible.

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihoodestimation and the Bayesian estimation of the model parameters are obtained based on dataaugmentation method. A simulation study based on proposed sampling algorithm is conductedto assess the performance of the proposed estimation for various sample sizes. Finally, two realdata-sets are analysed to illustrate the practicability of the proposed method.

基于计数模型方法的林分枯损研究

利用吉林省汪清林业局金沟岭林场落叶松林分连续观测数据,分别利用Poisson回归模型、负二项模型、零膨胀模型和Hurdle模型拟合林木枯损株数,并通过AIC值以及Vuong检验对这些模型进行详细分析比较。结果表明:Poisson回归模型不适用于模拟林木枯损株数,负二项回归模型相对于Poisson回归模型比较适用;但是对于零枯损过多的数据,这2类模型拟合效果较差。零膨胀模型和Hurdle模型对这类数据有很好的解决办法,其中,零膨胀负二项模型和Hurdle-NB模型拟合效果优于其他几种模型,且Hurdle-NB模型略好于零膨胀负二项模型。

黔南地区气象因子与森林火灾发生次数之间的关系

对黔南区春季防火期森林火灾数据进行分析,分别引入Poisson回归模型、负二项模型、零膨胀负二项模型和Hurdle模型拟合该地区火险天气森林火灾发生数,并对这些模型进行逐步筛选。结果表明:Poisson回归模型不适用于处理过度离散的数据,负二项回归模型相对于Poisson回归模型,比较适用于过离散数据;但是对于零个数过多的数据,这2类模型拟合效果较差,零膨胀负二项模型和Hurdle模型对这类数据有很好的解决办法。零膨胀负二项模型和Hurdle模型拟合效果优于其他2种模型,而且Hurdle模型好于零膨胀负二项模型。

广义线性模型在林火发生预报中的应用

首先介绍了国内外广义线性模型在林火发生预报中的应用,其次分别阐述了常用于林火发生预测的正态分布、逻辑斯蒂分布、泊松分布、负二项分布、零膨胀、栅栏等6种广义线性回归模型的表达式、参数估计方法和几种相关的假设检验方法,其中,逻辑斯蒂广义线性模型主要用于预测林火发生的概率,其他5种模型主要用于预测林火发生的频次。根据林火发生频次的数据结构特点和前人的研究结果分析得出,与正态分布相比,泊松分布、负二项分布、零膨胀、栅栏4种广义线性回归模型更适于预测林火发生的次数。当林火发生频次的方差接近于期望,应采用泊松或零膨胀泊松广义线性模型;如林火发生频次的方差显著大于期望,则宜采用负二项或零膨胀负二项广义线性模型。最后,对广义线性模型在我国林火发生预测中的应用提出了三方面建议:第一,增加模型的自变量(如森林可燃物特征、地形、人类活动等因子);第二,增加模型在景观层次林火发生预报中的应用;第三,拓展模型的建模方法,如建立广义线性混合效应模型和广义相加模型。

长白落叶松林分进界模型的研究

利用吉林省汪清林业局金沟岭林场落叶松林分连续观测数据,以计数类模型为基础,分别利用Poisson回归模型、负二项模型、零膨胀模型和Hurdle模型拟合林木进界株数,并通过AIC值,Pearson残差图以及Vuong检验对这些模型进行了详细分析比较。结果表明:Poisson回归模型不适用于模拟林木枯损株数;负二项回归模型相对于Poisson回归模型比较适用,但是对于零枯损过多的数据,这两类模型拟合效果较差;零膨胀模型和Hurdle模型对这类数据有很好的解决办法,而且,零膨胀负二项模型拟合效果最好。

古典风险模型的一个推广

将古典破产模型中按单位时间常数速率收取保险费的假设推广为保费收取过程为一复合Poisson过程,从而对古典的破产模型进行了推广,并给出了相应的Lundberg不等式及与古典模型中调节系数的比较.

保险系统中一类双险种风险模型的破产概率

本文研究了一类双险种风险模型,对此模型得到了最终破产概率的一般表达式和破产概率的一个上界估计.

索赔为稀疏过程的风险模型

保费收取过程为Poisson过程时 ,利用Poisson过程在随机选择下的不变性 ,讨论索赔为稀疏过程的风险模型的破产概率 ,并证明Lundberg不等式和破产概率的一般公式 .

零膨胀泊松模型的改进在零次索赔建模中的应用

零膨胀是非寿险精算中的一种常见现象,国内外许多学者对此进行了研究分析,而最具影响力的方法是零膨胀泊松模型与Hurdle模型,但这两个方法在区分零之间的差别时存在不足。实际中,产生零次索赔的保单持有人并非全部同质,如何提取零中所包含的信息对保险公司来说是重要的。鉴此,基于零膨胀泊松模型与Hurdle模型的思想,提出修正的零膨胀泊松模型,并利用非寿险精算中的实际数据,对新模型进行了拟合分析。与零膨胀泊松模型拟合结果的比较说明,修正的零膨胀模型在零的处理上更符合实际情况,更能体现零中所包含的信息。

带常利率和干扰项的负风险模型相关性质

为解决基本负风险模型与保险公司实际运营的偏差问题,在考虑了其他因素影响的前提下,建立了同时含有常利率和干扰项的负风险模型,使其更加贴近保险公司及经营性公司的实际情况.首先采用矩母函数的定义及相关性质推导了新模型的基本性质,介绍了调节系数的概念,然后利用切比雪夫不等式证明了新模型破产概率的表达式以及破产概率所满足的Lundberg上界,最后通过数值模拟,分别分析了两种因素对新模型破产概率上界的影响.结果表明:在干扰项不变的情况下,新模型的破产概率上界会随着利率的增加而减小;在利率不变的情况下,破产概率上界会随着随机因素的干扰而变大.该成果对保险公司的实际运营具有一定的指导意义.

零膨胀模型在非寿险中应用

分类费率厘定中最常使用的模型之一是泊松回归模型,但当损失次数数据存在零膨胀特征时,通常会采用零膨胀模型来解决。本文讨论一些零膨胀模型在非寿险中的应用,并通过对一组汽车保险损失数据的拟合,发现零膨胀模型可以有效改善对实际损失数据的拟合效果。

稀疏过程在带干扰的多险种风险模型中的应用

利用Poisson过程在随机选择下的不变性,讨论带干扰的索赔为稀疏过程的多险种风险模型的破产概率,并证明Lundberg不等式Ψ(u)≤e-Ru和破产概率的一般公式Ψ(u)=E[exp(-RRe(-TRuu))Tu<∞]成立.