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).