Investigating Hill’s question for some probability distributions

Abstract

Benford’s law asserts that the lower first significant digit (FSD) occurs more frequently than the higher FSD in naturally produced datasets. The applications of the law vary from detecting election, tax, and Covid-19 data fraud to checking abnormalities in the stock market. Hence, it is vital to know which common probability distributions satisfy Benford’s law, which is called Hill’s question. Many research studies have been performed to answer this question by using various methods. The purpose of the work is to give a more simple and intuitive method to address the question for some common probability distributions. Moreover, statistical simulation is adopted to test their conformity to Benford’s law.