Extreme Value Theory
4. Block maxima results – examples of
different limiting behaviour
[this page | pdf | references | back links]
Return
to Abstract and Contents
The limiting behaviours of many traditional distributions
are well-known. For example, block maxima values for the normal, log-normal and exponential
distributions converge to the Gumbel
distribution. Those for the Student’s t,
inverse gamma,
F and Pareto
distributions converge to the Fréchet
distribution.
Two examples where it is easy to derive the limiting
distributions are the exponential and the Pareto distribution:
Exponential
Suppose the underlying distribution is an exponential
distribution with distribution function for
and
.
Then by choosing normalising sequences and
we
have:
So .
Pareto
Suppose the underlying distribution is a Pareto distribution
with
distribution function for
and
.
Then by choosing the normalising sequences and
we
have:
So .
NAVIGATION LINKS
Contents | Prev