Extreme value theory

related topics
{theory, work, human}
{rate, high, increase}
{math, number, function}
{company, market, business}

Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions. The general theory sets out to assess the type of probability distributions generated by processes. Extreme value theory is important for assessing risk for highly unusual events, such as 100-year floods.

Contents

Approaches

Two approaches exist today:

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, called Peak Over Threshold models (POT). 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 used for cases where Theorem I applies, which creates 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 independent random variables from the same arbitrary distribution. Emil Julius 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:

Full article ▸

related documents
Classism
Forgetting curve
Satisficing
Alfred Marshall
Kenneth Arrow
Ultrafinitism
Finitism
Vladimir Arnold
Christoph Gottfried Bardili
William Schutz
Term logic/Danielsavoiu's summary
Adage
Wikipedia:WikiProject Military history/Arab-Israeli conflict general remarks
Painting style
Collective unconscious
Absurdist fiction
Institutional Mode of Representation
Bahya ibn Paquda
Denying the antecedent
Chaos argument
Hippodamus of Miletus
Orgel's rule
Dominator culture
Harold Lasswell
Ki Society
The Age of Spiritual Machines
Conceptual schema
Chindōgu
Reproductive technology
Queer studies