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Statistical Inference for Traffic Safety Analysis Using the Generalized Pareto Distribution

Sara, Emilsson LU and Vestin, Filip LU (2020) In Master's Theses in Mathematical Sciences MASM01 20201
Mathematical Statistics
Abstract (Swedish)
This thesis investigates the possibility of computing interval estimates for metrics that pertain to traffic safety based on surrogate measures of safety. A probabilistic model of the (near) crash count is defined using the generalized Pareto distribution and three different methods for calculating confidence intervals for the corresponding intensity parameter are proposed. We consider the delta method, the profile likelihood and a modification to the profile likelihood. Using the same methods we construct statistical tests in order to compare the safety of two infrastructure designs controlling for difference in traffic flow. These methods are then applied to three data sets from intersections in Denmark and three intersections in the... (More)
This thesis investigates the possibility of computing interval estimates for metrics that pertain to traffic safety based on surrogate measures of safety. A probabilistic model of the (near) crash count is defined using the generalized Pareto distribution and three different methods for calculating confidence intervals for the corresponding intensity parameter are proposed. We consider the delta method, the profile likelihood and a modification to the profile likelihood. Using the same methods we construct statistical tests in order to compare the safety of two infrastructure designs controlling for difference in traffic flow. These methods are then applied to three data sets from intersections in Denmark and three intersections in the Netherlands. Our findings show that the profile likelihood method yields satisfactory results in comparison to the other two methods; while also being relatively straightforward to implement. (Less)
Please use this url to cite or link to this publication:
author
Sara, Emilsson LU and Vestin, Filip LU
supervisor
organization
course
MASM01 20201
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Extreme value theory, traffic safety analysis, surrogate measure of safety, maximum likelihood, delta method, profile likelihood, modified profile likelihood.
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMS-3096-2020
ISSN
1404-6342
other publication id
2020:E73
language
English
id
9029968
date added to LUP
2020-10-05 13:33:15
date last changed
2021-06-08 17:21:18
@misc{9029968,
  abstract     = {{This thesis investigates the possibility of computing interval estimates for metrics that pertain to traffic safety based on surrogate measures of safety. A probabilistic model of the (near) crash count is defined using the generalized Pareto distribution and three different methods for calculating confidence intervals for the corresponding intensity parameter are proposed. We consider the delta method, the profile likelihood and a modification to the profile likelihood. Using the same methods we construct statistical tests in order to compare the safety of two infrastructure designs controlling for difference in traffic flow. These methods are then applied to three data sets from intersections in Denmark and three intersections in the Netherlands. Our findings show that the profile likelihood method yields satisfactory results in comparison to the other two methods; while also being relatively straightforward to implement.}},
  author       = {{Sara, Emilsson and Vestin, Filip}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Statistical Inference for Traffic Safety Analysis Using the Generalized Pareto Distribution}},
  year         = {{2020}},
}