The Lomax distribution, also called the Pareto Type II distribution, is a heavy-tail probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

 often used in business, economics, and actuarial modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero.

Probability density function

The pdf for the Lombax distribution is given by:
This can be rewritten in such a way that more clearly shows the relation to the Pareto distribution. That is:

Relation to the Pareto distribution

The Lomax distribution is the Pareto distribution shifted so that its support begins at zero. Specifically:

Relation to generalized Pareto distribution

The Lomax distribution is a special case of the generalized Pareto distribution. Specifically:

Relation to q-exponential distribution

The Lomax distribution is a special case of the q-exponential distribution. The q-exponential extends this distribution to support on a bounded interval. The lomax parameters are given by: