The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling.

It is essentially a Pareto distribution that has been shifted so that its support begins at zero.

[4] The probability density function (pdf) for the Lomax distribution is given by with shape parameter

The density can be rewritten in such a way that more clearly shows the relation to the Pareto Type I distribution.

, when the moment has the value The Lomax distribution is a Pareto Type I distribution shifted so that its support begins at zero.

Specifically: The Lomax distribution with scale parameter λ = 1 is a special case of the beta prime distribution.

The q-exponential extends this distribution to support on a bounded interval.

The Lomax parameters are given by: The logarithm of a Lomax(shape = 1.0, scale = λ)-distributed variable follows a logistic distribution with location log(λ) and scale 1.0.

If λ|k,θ ~ Gamma(shape = k, scale = θ) and X|λ ~ Exponential(rate = λ) then the marginal distribution of X|k,θ is Lomax(shape = k, scale = 1/θ).

Since the rate parameter may equivalently be reparameterized to a scale parameter, the Lomax distribution constitutes a scale mixture of exponentials (with the exponential scale parameter following an inverse-gamma distribution).