Breakdown of Benford’s law for birth data

Abstract

Long birth time series for Romania are investigated from Benford's law point of view, distinguishing between families with a religious (Orthodox and Non-Orthodox) affiliation. The data extend from Jan. 01, 1905 till Dec. 31, 2001, i.e. over 97 years or 35 429 days. The results point to a drastic breakdown of Benford's law. Some interpretation is proposed, based on the statistical aspects due to population sizes, rather than on human thought constraints when the law breakdown is usually expected. Benford's law breakdown clearly points to natural causes.

Effect of religious rules on time of conception in Romania from 1905 to 2001

“…97 years + 24 leap years) daily time series representing all births (24, 947,061) of persons alive at the 1992 or 2002 censuses (similar to Kestenbaum, 1987). Other long data series have been studied before (Cancho-Candela et al, 2007;Ausloos et al, 2015;Rotundo et al, 2015) using different methodologies. In the present case, data points were recorded for 01/01/1905 to 31/12/1991 (31,776 points) from the 1992 census, while the other 3,653 points (corresponding to the period 01/01/1992 to 31/12/2001) are from the 2002 census.…”

Benford's Law as an Indicator of Survey Reliability—can We Trust Our Data?

“…Authors who have used it to evaluate (survey) data quality include Judge and Schechter (), mainly for agricultural data; Nigrini and Miller (), for hydrological data; Sandron (), for population numbers; Mir (), for religious data; Ausloos et al . (), for long‐term birth numbers; Fu et al . (), for image forensics; and Swanson, Cho and Eltinge (), for consumption expenditures.…”

“…This rule, however commonly used by tax authorities to detect fraud, is still not widely applied in social sciences. 3 Authors who have used it to evaluate (survey) data quality include Judge and Schechter (2009), mainly for agricultural data; Nigrini and Miller (2007), for hydrological data; Sandron (2002), for population numbers; Mir (2014), for religious data; Ausloos et al (2015), for long-term birth numbers; Fu et al (2007), for image forensics; and Swanson, Cho and Eltinge (2003), for consumption expenditures. Additionally, further studies exist that discuss the use of Benford´s law as a lie detector (Gauvrit et al, 2017), to detect incorrect information of countries regarding their effort to combat money laundering (Deleanu, 2017), or to assess the reliability of financial reports in developing countries (Shi et al, 2018).…”

Benford’s law, its applicability and breakdown in the IR spectra of polymers

“…Engel et al demonstrated that the Benford law takes place approximatively for exponentially distributed numbers [14]. The breakdown of the Benford law was reported for certain sets of statistical data [15][16].…”