Frequently Asked Questions In Quantitative Finance

Chapter 3: The Most Popular Probability Distributions 241

Mean

a+b

2

.

Variance

(b−a)^2

12

.

Inverse normal Bounded below, unbounded above. It has

two parameters:a>0, location;b>0 scale. Its proba-

bility density function is given by

√

b

2 πx^3

e

− 2 bx

(

x−a

a

) 2

x≥ 0.

This distribution models the time taken by a Brownian

Motion to cover a certain distance.

Inverse normal

0

0.2

0.4

0.6

0.8

1

1.2

00.511.522.533.54

a = 1

b = 4