Extreme Value Distributions
EasyFit
: select the best fitting distribution and use it to make better decisions.
learn more
The problem of modeling extreme or rare events arises in many areas where such events can have very
negative consequences. Some examples of rare events include extreme floods and snowfalls, high wind
speeds, extreme temperatures, large fluctuations in exchange rates, and market crashes. To develop
appropriate probabilistic models and assess the risks caused by these events, business analysts and
engineers frequently use the extreme value distributions (EVD).
Contents
Extreme
Value
Theory
Gumbel
Distribution
(EVD
Type
I)
Fréchet
Distribution
(EVD
Type
II)
Weibull
Distribution
(EVD
Type
III)
Generalized
Extreme
Value
Distribution
Using Extreme Value Distributions in EasyFit
Extreme Value Theory
Extreme value theory
is a separate branch of statistics that deals with extreme events. This theory is based
on the
extremal types theorem
, also called the
three types theorem
, stating that there are only three types of
distributions that are needed to model the maximum or minimum of the collection of random observations
from the same distribution.
In other words, if you generate N data sets from the same distribution, and create a new data set that
includes the maximum values from these N data sets, the resulting data set can
only
be described by one of
the three models  specifically, the
Gumbel
,
Fréchet
, and
Weibull
distributions.
These models, along with the
Generalized Extreme Value
distribution, are widely used in risk management,
finance, insurance, economics, hydrology, material sciences, telecommunications, and many other
industries dealing with extreme events.
top
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentGumbel Distribution
One of the first scientists to apply the theory was a German mathematician Emil Gumbel (18911966).
Gumbel's focus was primarily on applications of extreme value theory to engineering problems, in
particular modeling of meteorological phenomena such as annual flood flows:
"It seems that the rivers know the theory. It only remains to convince the engineers of the validity of this
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '08
 Staff
 Extreme value, Weibull distribution, Generalized extreme value distribution, Emil Gumbel

Click to edit the document details