# Про масштабну інваріантність і кризу єврозони

09/24/2011 | loup-garou

Fact and Fiction in EU-Governmental Economic Data

http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract

>

http://en.wikipedia.org/wiki/Benford%27s_law

> Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

> This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

....

> In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results. Following this idea, Mark Nigrini showed that Benford's law could be used as an indicator of accounting and expenses fraud. In the United States, evidence based on Benford's law is legally admissible in criminal cases at the federal, state, and local levels.

http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract

>

**Abstract**. To detect manipulations or fraud in accounting data, auditors have successfully used Benford's law as part of their fraud detection processes. Benford's law proposes a distribution for first digits of numbers in naturally occurring data. Government accounting and statistics are similar in nature to financial accounting. In the European Union (EU), there is pressure to comply with the Stability and Growth Pact criteria. Therefore, like firms, governments might try to make their economic situation seem better. In this paper, we use a Benford test to investigate the quality of macroeconomic data relevant to the deficit criteria reported to Eurostat by the EU member states. We find that the data reported by Greece shows the greatest deviation from Benford's law among all euro states.http://en.wikipedia.org/wiki/Benford%27s_law

> Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 about 30% of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on the logarithmic scale.

> This counter-intuitive result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.

....

> In 1972, Hal Varian suggested that the law could be used to detect possible fraud in lists of socio-economic data submitted in support of public planning decisions. Based on the plausible assumption that people who make up figures tend to distribute their digits fairly uniformly, a simple comparison of first-digit frequency distribution from the data with the expected distribution according to Benford's law ought to show up any anomalous results. Following this idea, Mark Nigrini showed that Benford's law could be used as an indicator of accounting and expenses fraud. In the United States, evidence based on Benford's law is legally admissible in criminal cases at the federal, state, and local levels.