Dagum distribution


The Dagum distribution is a continuous probability distribution defined over positive real numbers. It is named after Camilo Dagum, who proposed it in a series of papers in the 1970s. The Dagum distribution arose from several variants of a new model on the size distribution of personal income and is mostly associated with the study of income distribution. There is both a three-parameter specification and a four-parameter specification of the Dagum distribution; a summary of the genesis of this distribution can be found in "A Guide to the Dagum Distributions". A general source on statistical size distributions often cited in work using the Dagum distribution is Statistical Size Distributions in Economics and Actuarial Sciences.

Definition

The cumulative distribution function of the Dagum distribution is given by
The corresponding probability density function is given by
The quantile function is given by
The Dagum distribution can be derived as a special case of the generalized Beta II distribution :
There is also an intimate relationship between the Dagum and Singh–Maddala distribution.
The cumulative distribution function of the Dagum distribution adds a point mass at the origin and then follows a Dagum distribution over the rest of the support

Use in economics

The Dagum distribution is often used to model income and wealth distribution. The relation between the Dagum Type I and the gini coefficient is summarized in the formula below:
where is the gamma function. Note that this value is independent from the scale-parameter,.
Although the Dagum distribution is not the only three parameter distribution used to model income distribution it is usually the most appropriate.