Wang Yao

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Extreme Value Theory (EVT) Application to Runway
Safety

• Wang Yao
• Department of Statistics
• Rutgers University
• wyao_at_eden.rutgers.edu
• Mentor Professor Regina Y. Liu

DIMACS -- July 17, 2008
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Motivation
allow multiple runway usage to ease air traffic
congestion!
Task
Cut-off point
Require all landings to be completed before the
cut-off point with certain guarantee

X
s
Q How to determine s such that P(Xgt s)
.0000001
(Extremely small!)
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Difficulty (why Extreme Value Theory)

• Extremely small tail probability
• e.g. p 0.0000001
• Few or no occurrences (observations) in reality
• e.g. Even with sample size2000

Difficulty No observations!
Possible Solution Extreme Value Theory (EVT)
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Overview of EVT
Random sample from unknown distr. fun. F
Order statistics
Tail index ? Characterizes tail thickness of F
Fréchet distribution heavy tail

Gumbel distribution in between, e.g. normal
dist.
Weibull distribution finite end point,
e.g. uniform dist.
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Extreme Quantile
For want to find
s.t.
Let
Take with , then
Estimated by
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Learning from Some Known Distributions
e.g. Normal, Exponential, Chi-square,

• Generate random samples
• For p 0.001, estimate the p-th upper quantile
• Analysis
• Bootstrap Method
• a resampling technique for obtaining
• limiting distribution of any estimator

Small sample size
Method of moments
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Real Data
underling distribution/model unknown!
e.g. Landing distance
Task Applying Bootstrap Method to find a proper
k (Bootstrap method completely nonparametric
approach and does not need to know the underlying
distribution)
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Yet to be completed

• Analyze landing data collected from airport
  runways
• Apply bootstrap method with proper choice of k
• Determine the suitable cut-off point --
• estimate the tail index , and extreme
  quantile
• Remarks

Important project with real application.
Well motivated and requires new interesting
statistical methodology
I learned some interesting new subjects, e.g.
EVT, bootstrap method.
Statistics is a practical field and theoretically
challenging.
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• Questions?

Acknowledgment Thanks to DIMACS REU!