AN OVERVIEW OF THE DISTRIBUTIONS OF CLAIMS USED IN NON-LIFE INSURANCE THAT CONFORM TO BENFORD'S LAW

Abstract

<p>Benford's law, known as the law of the first digit, is used as a basic method to identify possible manipulation, or errors dеtection, in a large data set. Namely, according to that law, the first digits of the corresponding data set appear with a frequency determined according to the decreasing logarithmic law, which is contrary to the intuition about their uniform appearance. Thus, the number 1 appears in approximately 30% of the cases as the first digit, while the number 9 appears in 4.58% of cases. The subject of the paper is an overview of  distributions that conform to Benford's law, which is confirmed both theoretically (by proving the theorems) and empirically (by conducting simulations). The goal of the paper is to determine the distribution that best fits the data on non-life insurance claims and then to examine the agreement with Benford's law using statistical tests applied in the literature. The main result of the paper is to determine the agreement or disagreement of the observed data set with Benford's law, thus providing an answer to the question about their possible manipulation and a possible proposal for a deeper analysis of individual numbers.</p>