Frequently Asked Questions In Quantitative Finance

236 Frequently Asked Questions In Quantitative Finance

Mean

ν+a.

Variance

2(ν+ 2 a).

Gumbel Unbounded above and below. It has two param-

eters:a, location;b>0 scale. Its probability density

function is given by

1

b

e

a−x

b e−e

a−x

b.

The Gumbel distribution is useful for modelling extreme

values, representing the distribution of the maximum

value out of a large number of random variables drawn

from an unbounded distribution.

Gumbel

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-4 -3 -2 -1 0 1 2 3 4

a = -1

b = 1