A.16 Pareto distribution

X has a Pareto distribution with parameters and γ, denoted

if it has density

where

is the indicator function of the set . The mean and variance are

The distribution function is

and in particular the median is

The mode, of course, occurs at

The ordered pair (Y, Z) has a bilateral bivariate Pareto distribution with parameters , η and γ, denoted

if it has joint density function

The means and variances are

and the correlation coefficient between Y and Z is

It is also sometimes useful that

The marginal distribution function of Y is

and in particular the median is

The distribution function of Z is similar, and in particular the median is

The modes, of course, occur at

The distribution is discussed in DeGroot (1970, Sections 4.11, 5.7 and 9.7).