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Wang Yao Department of Statistics Rutgers University wyao@eden.rutgers

Extreme Value Theory (EVT): Application to Runway Safety. Wang Yao Department of Statistics Rutgers University wyao@eden.rutgers.edu Mentor: Professor Regina Y. Liu. DIMACS -- July 17, 2008. Motivation. Task :.

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Wang Yao Department of Statistics Rutgers University wyao@eden.rutgers

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  1. Extreme Value Theory (EVT): Application to Runway Safety Wang Yao Department of Statistics Rutgers University wyao@eden.rutgers.edu Mentor: Professor Regina Y. Liu DIMACS -- July 17, 2008

  2. Motivation Task: allow multiple runway usageto ease air traffic congestion! Cut-off point: Require all landings to be completed before the cut-off point with certain “guarantee” * X s Q:How to determine ssuch that: P(X>s) .0000001= (Extremely small!)

  3. 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 size=2000 Difficulty:No observations! Possible Solution: Extreme Value Theory (EVT)

  4. 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.

  5. Extreme Quantile Forwant to finds.t. Let Take with , then Estimated by

  6. 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

  7. Real Data e.g. Landing distance: underling distribution/model unknown! Task:ApplyingBootstrap Method to find a proper k (Bootstrap method: completely nonparametric approach and does not need to know the underlying distribution)

  8. 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 -- estimatethe 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.

  9. Questions? Acknowledgment: Thanks to DIMACS REU!

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