Frequently Asked Questions In Quantitative Finance

Chapter 3: The Most Popular Probability Distributions 243

Mean

a+bc.

Variance

b^2 c.

Logistic This distribution is unbounded below and above.

It has two parameters:a, location;b>0 scale. Its prob-

ability density function is given by

1

b

e

x−a

b

(

1 +e

x−a

b

) 2.

The logistic distribution models the mid value of highs

and lows of a collection of random variables, as the

number of samples becomes large.

Mean

a.

Logistic

0

0.05

0.1

0.15

0.2

0.25

0.3

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

a = -2

b = 1