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We introduce an iterative discrete information production process where wecan extend ordered normalised vectors by new elements based on a simple affinetransformation, while preserving the predefined level of inequality, G, asmeasured by the Gini index.  Then, we derive the family of empirical Lorenz curves of the correspondingvectors and prove that it is stochastically ordered with respect to both thesample size and G which plays the role of the uncertainty parameter. We provethat asymptotically, we obtain all, and only, Lorenz curves generated by a new,intuitive parametrisation of the finite-mean Pickands' Generalised ParetoDistribution (GPD) that unifies three other families, namely: the Pareto TypeII, exponential, and scaled beta distributions. The family is not only totallyordered with respect to the parameter G, but also, thanks to our derivations,has a nice underlying interpretation. Our result may thus shed a new light onthe genesis of this family of distributions.  Our model fits bibliometric, informetric, socioeconomic, and environmentaldata reasonably well. It is quite user-friendly for it only depends on thesample size and its Gini index.

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution