Accounting for Heterogeneity in Stop Frequency Models of Work Tours Using Latent Class Poisson Models

Stop frequency models, as one of the elements of activity based models, represent an important part of travel behavior. Unobserved heterogeneity across the travelers should be taken into consideration to prevent biasedness and inconsistency in the estimated parameters in the stop frequency models. Additionally, previous studies on the stop frequency have mostly been done in larger metropolitan areas and less attention has been paid to the areas with less population. This study addresses these gaps by using 2012 travel data from a medium sized U.S. urban area using the work tour for the case study. Stop in the work tour were classified into three groups of outbound leg, work based subtour, and inbound leg of the commutes. Latent Class Poisson Regression Models were used to analyze the data. The results indicate the presence of heterogeneity across the commuters. Using latent class models significantly improves the predictive power of the models compared to regular one class Poisson regression models. In contrast to one class Poisson models, gender becomes insignificant in predicting the number of tours when unobserved heterogeneity is accounted for. The commuters are associated with increased stops on their work based subtour when the employment density of service-related occupations increases in their work zone, but employment density of retail employment does not significantly contribute to the stop making likelihood of the commuters. Additionally, an increase in the number of work tours was associated with fewer stops on the inbound leg of the commute. The results of this study suggest the consideration of unobserved heterogeneity in the stop frequency models and help transportation agencies and policy makers make better inferences from such models.

Model test of negative Poisson’s ratio cable for supporting super-largespan tunnel using excavation compensation method

In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。

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].

Poisson截断δ冲击模型失效参数的Bayes估计

针对Poisson截断δ冲击模型失效参数的估计问题,利用Bayes估计方法,在最小均方误差原则下,基于寿命终止时总冲击次数及冲击到达时间这两类样本数据,在不同的先验假设下,给出Poisson截断δ冲击模型失效参数δ的Bayes估计量.

Using Poisson Modeling and Queuing Theory to Optimize Staffing and Decrease Patient Wait Time in the Emergency Department

Introduction: Studies have shown Emergency Department (ED) crowding contributes to reduced quality of patient care, delays in starting treatments, and increased number of patients leaving without being seen. This analysis shows how to theoretically and optimally align staffing to demand. Methods: The ED value stream was identified and mapped. Patients were stratified into three resource-driven care flow cells based on the severity indices. Time observations were conducted for each of the key care team members and the manual cycle times and service rate were calculated and stratified by severity indices. Using X32 Healthcare’s Online Staffing Optimization (OSO) tool, staffing inefficiencies were identified and an optimal schedule was created for each provider group. Results: Lower Severity Indices (higher acuity patient) led to longer times for providers, nurses, patient care assistants, and clerks. The patient length of stay varied from under one hour to over five hours. The flow of patients varied considerably over the 24 hours’ period but was similar by day of the week. Using flow data, we showed that we needed more nurses, more care team members during peak times of patient flow. Eight hour shifts would allow better flexibility. We showed that the additional salary hours added to the budget would be made up for by increased revenue recognized by decreasing the number of patients who leave without being seen. Conclusion: If implemented, these changes will improve ED flow by using lean tools and principles, ultimately leading to timeliness of care, reduced waits, and improved patient experience.

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.

Optimal Dividend Problem for a Compound Poisson Risk Model

In this note we study the optimal dividend problem for a company whose surplus process, in the absence of dividend payments, evolves as a generalized compound Poisson model in which the counting process is a generalized Poisson process. This model includes the classical risk model and the Pólya-Aeppli risk model as special cases. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that under some conditions the optimal dividend strategy is formed by a barrier strategy. Moreover, two conjectures are proposed.

Nonlinear Modeling for a Two-Stage Degradation System Based on Nonhomogeneous Poisson Process

The degradation process modeling is one of research hotspots of prognostic and health management(PHM),which can be used to estimate system reliability and remaining useful life(RUL).In order to study system degradation process,cumulative damage model is used for degradation modeling.Assuming that damage increment is Gamma distribution,shock counting subjects to a homogeneous Poisson process(HPP)when degradation process is linear,and shock counting is a non-homogeneous Poisson process(NHPP)when degradation process is nonlinear.A two-stage degradation system is considered in this paper,for which the degradation process is linear in the first stage and the degradation process is nonlinear in the second stage.A nonlinear modeling method for considered system is put forward,and reliability model and remaining useful life model are established.A case study is given to validate the veracities of established models.

Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model

In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.

Comparison of Ruin Probabilities in Compound Poisson Risk Model

Compound Poisson risk model has been simulated. It has started with exponential claim sizes. The simulations have checked for infinite ruin probabilities. An appropriate time window has been chosen to estimate and compare ruin probabilities. The infinite ruin probabilities of two-compound Poisson risk process have estimated and compared them with standard theoretical results.

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars.

The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio（LURR） of different definitions（Y1～Y5）using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y1～Y5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large（】40）;but when this occurrence ratebecomes very small,Y2～Y5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y1 and Y3 are given in this paper,which is helpful to quantify the random

Analysis of Ozone Behaviour in the City of Puebla-Mexico Using Non-Homogeneous Poisson Models with Multiple Change-Points

In this work, some non-homogeneous Poisson models are considered to study the behaviour of ozone in the city of Puebla, Mexico. Several functions are used as the rate function for the non-homogeneous Poisson process. In addition to their dependence on time, these rate functions also depend on some parameters that need to be estimated. In order to estimate them, a Bayesian approach will be taken. The expressions for the distributions of the parameters involved in the models are very complex. Therefore, Markov chain Monte Carlo algorithms are used to estimate them. The methodology is applied to the ozone data from the city of Puebla, Mexico.

Comparing the Adequacy of Some Non-Homogeneous Poisson Models to Estimate Ozone Exceedances in Mexico City

We consider some non-homogeneous Poisson models to estimate the mean number of times that a given environmental threshold of interest is surpassed by a given pollutant. Seven different rate functions for the Poisson processes describing the models are taken into account. The rate functions considered are the Weibull, exponentiated-Weibull, and their generalisation the Beta-Weibull rate function. We also use the Musa-Okumoto, the Goel-Okumoto, a generalised Goel- Okumoto and the Weibull-geometric rate functions. Whenever thought justifiable, the model allowing the presence of change-points is also going to be considered. The different models are applied to the daily maximum ozone measurements data provided by the monitoring network of the Metropolitan Area of Mexico City. The aim is to compare the adjustment of different rate functions to the data. Even though, some of the rate functions have been considered before, now we are applying them to the same data set. In previous works they were used in different data sets and therefore a comparison of the adequacy of those models were not possible. The measurements considered here were obtained after a series of environmental measures were implemented in Mexico City. Hence, the data present a different behaviour from that of earlier studies.

Robust Estimators for Poisson Regression

The present paper proposes a new robust estimator for Poisson regression models. We used the weighted maximum likelihood estimators which are regarded as Mallows-type estimators. We perform a Monte Carlo simulation study to assess the performance of a suggested estimator compared to the maximum likelihood estimator and some robust methods. The result shows that, in general, all robust methods in this paper perform better than the classical maximum likelihood estimators when the model contains outliers. The proposed estimators showed the best performance compared to other robust estimators.

One-Sample Bayesian Predictive Analyses for a Nonhomogeneous Poisson Process with Delayed S-Shaped Intensity Function Using Non-Informative Priors

The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.

耦合均值-相关性的起重伤害事故致因ZIP模型研究

近些年来,起重伤害事故高发频发,导致了较大的直接经济损失和人员伤亡,受到行业的高度关注。为探究起重伤害事故致因的影响程度,采集2011—2021年376份起重伤害事故调查报告,依据事故致因24Model和系统安全分析法识别事故致因,构建起重伤害事故致因的零膨胀泊松回归模型(Zero-Inflated Poisson,ZIP),并通过Vuong方法和拟合优度检验准则进行检验;综合考虑事故致因发生频次的均值、致因和事故发生的相关性,运用弹性分析方法对事故致因的影响程度进行定量排序。结果表明:ZIP回归模型拟合效果优于泊松回归模型,各事故致因对起重伤害事故的影响程度排序为安全监管不到位C_(6)(T_(k)=1.0221)、安全意识淡薄H_(1)(T_(k)=0.5117)、作业人员违规作业H_(3)(T_(k)=0.4758)、作业人员无证上岗H_(2)(T_(k)=0.2116)、专项施工方案不合格C_(7)(T_(k)=0.1234)和结构构件破坏或连接不可靠M_(3)(T_(k)=0.1045)。研究从事故致因发生频次的均值、致因和事故发生的相关性两个维度刻画事故致因对起重伤害事故的影响程度,为起重伤害事故风险分级管控提供了新的研究思路和方法。