Frequently Asked Questions In Quantitative Finance

Chapter 3: The Most Popular Probability Distributions 237

Mean

a+γb,

whereγis Euler’s constant, 0.577216....

Variance

1

6

π^2 b^2.

Weibull Bounded below and unbounded above. It has

three parameters:a, location;b>0, scale;c>0, shape.

Its probability density function is given by

c

b

(

x−a

b

)c− 1

exp

(

−

(

x−a

b

)c)

, x>a.

The Weibull distribution is also useful for modelling

extreme values, representing the distribution of the max-

imum value out of a large number of random variables

Weibull

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 1.5 2 2.5 3 3.5 4

a = 1

b = 1

c = 2