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Technical Paper

Application of Extreme Value Theory to Crash Data Analysis

2017-11-13
2017-22-0011
A parametric model obtained by fitting a set of data to a function generally uses a procedure such as maximum likelihood or least squares. In general this will generate the best estimate for the distribution of the data overall but will not necessarily generate a reasonable estimation for the tail of the distribution unless the function fitted resembles the underlying distribution function. A distribution function can represent an estimate that is significantly different from the actual tail data, while the bulk of the data is reasonably represented by the central part of the fitted distribution. Extreme value theory can be used to improve the predictive capabilities of the fitted function in the tail region. In this study the peak-over-threshold approach from the extreme value theory was utilized to show that it is possible to obtain a better fit of the tail of a distribution than the procedures that use the entire distribution only.
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