New Estimation Technique for Vehicle-Type-Specific Headway Distributions

1998 ◽  
Vol 1646 (1) ◽  
pp. 18-28 ◽  
Author(s):  
Serge P. Hoogendoorn ◽  
Piet H. L. Bovy
Keyword(s):  
Real Life ◽  
Estimation Procedure ◽  
Distribution Model ◽  
Parameter Estimates ◽  
Passenger Cars ◽  
Car Following ◽  
Vehicle Type ◽  
Real Life Data ◽  
Headway Distribution ◽  
Parameter Values

Recently, a new statistical procedure was developed that enables fast, accurate, and robust estimation of composite headway distributions, such as Branston’s generalized queueing model (GQM). Until now, the new procedure had only been applied to aggregate vehicular flow. In this paper, the estimation procedure is extended to headway observations segregated according to vehicle type and period of the day. Consequently, the parameters of a new mixed-vehicle-type headway distribution model based on Branston’s headway model can be estimated. Distinction of vehicle type and sample periods provides additional insight into the plausibility of the headway distributions and parameter values, as well as into the car-following behavior of the distinct vehicle classes varying across the different periods. The estimation procedure was applied to traffic data collected on a two-lane rural road in the Netherlands. Comparison of the estimated headway distributions with real-life data shows that headway distributions can be realistically replicated with the Pearson-III-based mixed-vehicle-type GQM. Inter-pretable differences between the morning, noon, and evening sample periods and between passenger cars, unarticulated trucks, and articulated trucks are found. In addition, passenger-car equivalents for both articulated trucks and unarticulated trucks were determined from the parameter estimates.

scholarly journals EM Estimation for Zero- and k-Inflated Poisson Regression Model

Computation ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 94
Author(s):  
Monika Arora ◽  
N. Rao Chaganty
Keyword(s):  
Regression Model ◽  
Expectation Maximization ◽  
Real Life ◽  
Mixture Distribution ◽  
Distribution Model ◽  
Parameter Estimates ◽  
Stochastic Representation ◽  
Fundamental Properties ◽  
Real Life Data ◽  
Information Matrices

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we provide details for obtaining parameter estimates of the ZkIP regression model using the Expectation–Maximization (EM) algorithm for a given data. We derive the standard errors of the EM estimates by computing the complete, missing, and observed data information matrices. We present the analysis of two real-life data using the methods outlined in the paper.

scholarly journals Monitoring Robust Estimates for Compositional Data

2021 ◽  
Vol 50 (2) ◽  
pp. 16-37
Author(s):  
Valentin Todorov
Keyword(s):  
Compositional Data ◽  
Real Life ◽  
R Package ◽  
Diagnostic Tools ◽  
Data Set ◽  
Mahalanobis Distances ◽  
Robust Estimates ◽  
Real Life Data ◽  
Manufactured Exports ◽  
Parameter Values

In a number of recent articles Riani, Cerioli, Atkinson and others advocate the technique of monitoring robust estimates computed over a range of key parameter values. Through this approach the diagnostic tools of choice can be tuned in such a way that highly robust estimators which are as efficient as possible are obtained. This approach is applicable to various robust multivariate estimates like S- and MM-estimates, MVE and MCD as well as to the Forward Search in whichmonitoring is part of the robust method. Key tool for detection of multivariate outliers and for monitoring of robust estimates is the Mahalanobis distances and statistics related to these distances. However, the results obtained with thistool in case of compositional data might be unrealistic since compositional data contain relative rather than absolute information and need to be transformed to the usual Euclidean geometry before the standard statistical tools can be applied. Various data transformations of compositional data have been introduced in the literature and theoretical results on the equivalence of the additive, the centered, and the isometric logratio transformation in the context of outlier identification exist. To illustrate the problem of monitoring compositional data and to demonstrate the usefulness of monitoring in this case we start with a simple example and then analyze a real life data set presenting the technologicalstructure of manufactured exports. The analysis is conducted with the R package fsdaR, which makes the analytical and graphical tools provided in the MATLAB FSDA library available for R users.

scholarly journals Bayesian Analysis of Extended Cox Model with Time-Varying Covariates Using Bootstrap Prior

2020 ◽  
Vol 18 (2) ◽  
pp. 2-13
Author(s):  
Oyebayo Ridwan Olaniran ◽  
Mohd Asrul Affendi Abdullah
Keyword(s):  
Empirical Bayes ◽  
Cox Model ◽  
Real Life ◽  
Estimation Procedure ◽  
Time Varying ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Time Varying Covariates ◽  
Extended Cox Model

A new Bayesian estimation procedure for extended cox model with time varying covariate was presented. The prior was determined using bootstrapping technique within the framework of parametric empirical Bayes. The efficiency of the proposed method was observed using Monte Carlo simulation of extended Cox model with time varying covariates under varying scenarios. Validity of the proposed method was also ascertained using real life data set of Stanford heart transplant. Comparison of the proposed method with its competitor established appreciable supremacy of the method.

scholarly journals Impact of Dependence on Parameter Estimates of Autoregressive Process with Gumbel Distributed Innovation

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 365-380
Author(s):  
Sunday Samuel Bako ◽  
Mohd Bakri Adam ◽  
Anwar Fitrianto
Keyword(s):  
Scale Parameter ◽  
Extreme Values ◽  
Real Life ◽  
Location Parameter ◽  
Autoregressive Process ◽  
Parameter Estimates ◽  
Distributed Data ◽  
Original Series ◽  
Real Life Data ◽  
Ar Process

Recent studies have shown that independent identical distributed Gaussian random variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a stationary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto (GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads to overestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate. Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the Gumbel-GPD shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an underestimation of the parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel-GPD.

scholarly journals An Extension of Log-Logistic Distribution for Analyzing Survival Data

2020 ◽  
pp. 789-801
Author(s):  
Aliya Syed Malik ◽  
S.P. Ahmad
Keyword(s):  
Survival Data ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Logistic Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

ANALYSIS OF CAR FOLLOWING HEADWAY ALONG MULTILANE HIGHWAY

2016 ◽  
Vol 78 (4) ◽  
Author(s):  
Mohd Erwan Sanik ◽  
Joewono Prasetijo ◽  
Ahmad Hakimi Mat Nor ◽  
Nor Baizura Hamid ◽  
Ismail Yusof ◽  
...  
Keyword(s):  
Regression Models ◽  
Processing Technique ◽  
Image Processing Technique ◽  
Linear Regression Models ◽  
Car Following ◽  
Vehicle Type ◽  
Field Data Collection ◽  
Headway Distribution ◽  
Heavy Goods Vehicles ◽  
Linear Regressions

This study describes driver’s car following headway on multilane highways.  The aim of this study is to analyse the driver’s car following headway along multilane highway at four selected locations.  The objectives of this study were to determine car headway at Jalan Batu Pahat – Ayer Hitam multilane highway and to develop linear regression models to present the relationships between headway and speed.  Videotaping method was used in field data collection during peak hours.  Data were extracted from recorded video by using the image processing technique software.  The distance headways and associated vehicles speeds were classified into vehicle following category by vehicle type: car following car, car following heavy goods vehicle, heavy goods vehicle following heavy goods vehicle and heavy goods vehicle following car categories.  Linear regressions models were used to develop the relationships between headway and speed. Based on all headway distribution, it is found that patterns of the vehicle headways at four study locations were similar, which shown a significant number of the vehicles travel at headways less than 5 seconds.  Furthermore, it can be concluded that many drivers tend to follow the vehicles ahead closely on multilane highways.  The regression models were significantly reliable based on their R-square values which are ranging between 0.80 and 0.95.  From the analysis, cars were found to maintain larger headways when following heavy goods vehicles compare to when following other cars.

scholarly journals Analysis of Vehicle-Following Heterogeneity Using Self-Organizing Feature Maps

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Yang ◽  
Ruey Long Cheu ◽  
Xiucheng Guo ◽  
Alicia Romo
Keyword(s):  
Relative Velocity ◽  
Data Sets ◽  
Feature Maps ◽  
Passenger Cars ◽  
Passenger Car ◽  
Feature Map ◽  
Car Following ◽  
Vehicle Type ◽  
Vehicle Trajectories ◽  
Self Organizing

A self-organizing feature map (SOM) was used to represent vehicle-following and to analyze the heterogeneities in vehicle-following behavior. The SOM was constructed in such a way that the prototype vectors represented vehicle-following stimuli (the follower’s velocity, relative velocity, and gap) while the output signals represented the response (the follower’s acceleration). Vehicle trajectories collected at a northbound segment of Interstate 80 Freeway at Emeryville, CA, were used to train the SOM. The trajectory information of two selected pairs of passenger cars was then fed into the trained SOM to identify similar stimuli experienced by the followers. The observed responses, when the stimuli were classified by the SOM into the same category, were compared to discover the interdriver heterogeneity. The acceleration profile of another passenger car was analyzed in the same fashion to observe the interdriver heterogeneity. The distribution of responses derived from data sets of car-following-car and car-following-truck, respectively, was compared to ascertain inter-vehicle-type heterogeneity.

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