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Extreme value statistics and its applications
Author
Lee, Kok Sonk
Supervisor
Phang, Rosalind Lay Ping
Abstract
An extreme value is the largest or the smallest value in a data set . As n tends to infinity , the largest or the smallest value of a sample size n has asymptotically one of the 3 Types of Extreme Value Distributions (EVD) : the Gurnbel Type I, the Frechet Type I1 or the Type III distribution.
We used the Generalized Extreme Value (GEV) Distribution ( Maritz and Munro, 1967 ) to solve extreme values for small as well as large samples . A graphical plot was first conducted. Sextile estimates are evaluated and are used to derive the MLE of the parameters.
In this exercise we demonstrated the use of Extreme Value Theory to solve problems in three major areas : Environment ( Ozone Concentration ) , Meteorological ( Rainfall ) and Hydrology ( Flood ) We have identified the type of Extreme Value Distribution (EVD) the sampled data belongs to and return periods were also computed.
The main objective of this exercise is to use Extreme Value Theory to analyze a new area - a sporting event (the men's l00 m in the Olympics ). Chatterjee (1982) analyze and predicted the Olympic winning times but not without errors. Our analysis consist of two parts . First we analyze the data from 1900 to 1976. Our findings showed that the error percentage for the return periods of 1984, 1988, 1992, 1996 Olympics was less than 1%. Our results suggested that Extreme Value Theory could be used as an alternative method to analyze the 100 m event and hence a sporting event. Secondly we analyze the data from 1900 to 1996. Our findings showed that it belongs to the Type I11 EVD and the lower limit is 9.20s . We have also calculated the return periods for the 2016 and 2096 Olympics which is 9.83 and 9.70 respectively.
We used the Generalized Extreme Value (GEV) Distribution ( Maritz and Munro, 1967 ) to solve extreme values for small as well as large samples . A graphical plot was first conducted. Sextile estimates are evaluated and are used to derive the MLE of the parameters.
In this exercise we demonstrated the use of Extreme Value Theory to solve problems in three major areas : Environment ( Ozone Concentration ) , Meteorological ( Rainfall ) and Hydrology ( Flood ) We have identified the type of Extreme Value Distribution (EVD) the sampled data belongs to and return periods were also computed.
The main objective of this exercise is to use Extreme Value Theory to analyze a new area - a sporting event (the men's l00 m in the Olympics ). Chatterjee (1982) analyze and predicted the Olympic winning times but not without errors. Our analysis consist of two parts . First we analyze the data from 1900 to 1976. Our findings showed that the error percentage for the return periods of 1984, 1988, 1992, 1996 Olympics was less than 1%. Our results suggested that Extreme Value Theory could be used as an alternative method to analyze the 100 m event and hence a sporting event. Secondly we analyze the data from 1900 to 1996. Our findings showed that it belongs to the Type I11 EVD and the lower limit is 9.20s . We have also calculated the return periods for the 2016 and 2096 Olympics which is 9.83 and 9.70 respectively.
Date Issued
1997
Call Number
QA276 Lee
Date Submitted
1997