| Extreme Value Theory |
Article Index for Extreme |
Website Links For Extreme |
Information AboutExtreme Value Theory |
| CATEGORIES ABOUT EXTREME VALUE THEORY | |
| actuarial science | |
| statistical theory | |
| emergency management | |
| SHOPPER'S DELIGHT | |
|
Two approaches exist today: # Most common at this moment is the Tail-fitting approach based on the Second Theorem In Extreme Value Theory (Theorem II Pickands (1975), Balkema and de Haan (1974)). # Basic theory approach as described in the book by Burry (reference 2). In general this conforms to the First Theorem In Extreme Value Theory (Theorem I Fisher and Tippett (1928), and Gnedenko (1943)). The difference between the two theorems is due to the nature of the data generation. For theorem I the data are generated in full range, while in theorem II data is only generated when it surpasses a certain threshold (POT's models or Peak Over Threshold ). The POT approach has been developed largely in the insurance business, where only losses (pay outs) above a certain threshold are accessible to the insurance company. Strangely this approach is often applied to theorem I cases which poses problems with the basic model assumptions. Extreme value distributions are the limiting distributions for the minimum or the maximum of a very large collection of Random Observation s from the same arbitrary distribution. Gumbel (1958) showed that for any well-behaved initial distribution (i.e., F(x) is continuous and has an inverse), only a few models are needed, depending on whether you are interested in the maximum or the minimum, and also if the observations are bounded above or below. APPLICATIONS Applications of extreme value theory include predicting the probability distribution of:
HISTORY OF EXTREME VALUE THEORY The field of extreme value theory was founded by the German mathematician, pacifist, and anti-Nazi campaigner Emil Julius Gumbel who described the Gumbel Distribution in the 1950s . REFERENCES
SEE ALSO
EXTERNAL LINKS
|