Lomax distribution

The shifted Pareto distribution is considered in the mathematical statistics probability distribution, which is particularly suitable for modeling of large losses, especially in industrial and reinsurance. Mathematically, these are a Pareto distribution whose distribution curve is shifted by a fixed parameter value, hence the name of this distribution is derived.

Definition

A continuous random variable satisfies the shifted Pareto distribution with parameters, and when the probability density

Possesses.

Properties

Expected value

The expected value is given by:

Variance

The variance can be specified as

Standard deviation

From the expected value and variance, the standard deviation is

Coefficient of variation

From expectation and variance one obtains the coefficient of variation

Skew

Results for the skewness

Characteristic function

The characteristic function for the shifted Pareto distribution can not be specified in closed form.

Moment generating function

The moment generating function for the shifted Pareto distribution can not be specified in closed form.