Over the last century Extreme Value Theory (EVT) has become an established collection of statistical methods for estimating the tails of distributions in a wide range of academic disciplines. In addition, the practice of over-bounding the tail probabilities, typically using Gaussian distributions, has been developed in recent years for modeling system uncertainty. This paper analyzes and implements the combination of EVT estimation using the Maximum Likelihood Estimator (MLE) and conservative overbounding. Moreover, quantifying the uncertainties of EVT estimation is paramount for successfully constructing overbounds. Our work primarily investigates these uncertainties through Monte Carlo simulations of a variety of distributions. After characterizing these uncertainties, an EVT-based overbounding approach is presented for a simple linear system. The results of this work show that an EVT-based approach can generate conservative overbounds using significantly less data than experiments alone.
|Original language||English (US)|
|Title of host publication||Proceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||10|
|State||Published - May 26 2016|
|Event||IEEE/ION Position, Location and Navigation Symposium, PLANS 2016 - Savannah, Georgia|
Duration: Apr 11 2016 → Apr 14 2016
|Name||Proceedings of the IEEE/ION Position, Location and Navigation Symposium, PLANS 2016|
|Other||IEEE/ION Position, Location and Navigation Symposium, PLANS 2016|
|Period||4/11/16 → 4/14/16|
Bibliographical notePublisher Copyright:
© 2016 IEEE.
- extreme value theory