Construction of Benford Random Variables: Generators and Seed Functions

TL;DR

This paper introduces two general methods for constructing Benford random variables, demonstrating that all such variables can be generated through these methods, which aids in understanding their properties and base dependency.

Contribution

The paper presents novel, general construction methods for Benford random variables, expanding the tools for their analysis and exploration.

Findings

Every Benford random variable can be constructed using the proposed methods.

The methods facilitate investigation into the base dependency of Benford variables.

The constructions help explore the nature and properties of Benford distributions.

Abstract

In this paper I describe two general methods of constructing a probability density function (pdf) of a Benford random variable, and show that the pdf of every Benford random variable may be constructed by these methods. These constructions are helpful in exploring the nature of Benford random variables, and may be used to investigate some issues of base dependency of Benford random variables.