Testing benford and universal laws on gambling and betting data in Romania

This study examines the integrity of financial statements within the Romanian gambling and betting industry, employing Benford's, Zipf’s and Universal Law and distribution distances tests. Data from the financial statements of active gambling and betting companies in 2013, classified under NACE code 9200, were analysed The primary focus was on the absolute values of declared gross profit or loss. Our analysis involved visual inspections, Chi-square tests, and the application of Zipf’s and Universal laws for distribution conformity. Results indicated that the empirical distributions of the first and second digits, as well as the combined first two digits of gross profit or loss, align with Benford's Law. Surprisingly, the distribution did not conform to the expected Zipf’s type but instead followed the specific pattern of the Universal law. Furthermore, while the Zipf’s model was not a fit, the Universal law effectively captured the distribution of the reported financial data, suggesting a power-law concentration of gross profit values in the industry.