Benfordův zákon

Abstract

The goal of this work is to present a phenomenon called Benford's Law. This law describes a unique non-uniform distribution of significant digits in various numerical mathematical objects and naturally occurring datasets. Distribution of significant digits in real life allows, by comparing collections of numbers with Benford's Law, to expose for example election and accounting frauds and in this way be even used as evidence. In this thesis, we will describe this unique distribution of Benford's Law and define some benford mathematical objects. Next we will analyze many unique properties, that will allow us to find collections of numbers that are following Benford's Law. We will discuss differential equations in context with Benford's Law and we will try to explain the occurance of Benford's Law in many collections of numbers. In the end we will present naturally occurring datasets, which we compare to Benford's Law.