Benford’s law applied to aerobiological data and its potential as a quality control tool

Abstract

Benford's phenomenological law gives the expected frequencies of the first significant digits of any given series of numbers. According to this law, the frequency of 1 is higher than that of 2; this in turn appears more often 3, and so on. Similarly, Benford's law can also be applied to the first two significant digits (i.e., from 10 to 99), and so on. Here, we show that gross data sets of daily pollen counts from three aerobiological stations (located in European cities with different features regarding vegetation and climatology) fit Benford's law for the first significant digits, but this is not always true for the data transformed by a correction factor used in aerobiological studies. That is to say, the biases introduced by rounding and lower and upper built-in limits in pollen counts are detected by Benford's law analysis. The analysis of the first two significant digits from transformed data is better explained by a Power law than Benford's law. We propose that Benford's law could be used as a quality control tool for numerical aerobiological data sets.

Benford analysis: A useful paradigm for spectroscopic analysis

“…Such datasets following Benford's law also emerge from a plethora of sources ranging from astrophysical [3], geographical [4], biological [5][6][7], seismographic [8], to financial topics [9,10]. In the past, inspecting violations of Benford's law have proven to be useful in detecting the cases of tax fraud [11] and election fraud [12].…”

Most linear flows on Rd are Benford

“…Ever since first recorded by Newcomb [28] in 1881 and re-discovered by Benford [3] in 1938, examples of data and systems conforming to (1.1) in one form or another have been discussed extensively, notably for real-life data (e.g. [15,29]) as well as in stochastic (e.g. [30]) and deterministic processes (e.g.…”

Do τ lepton branching fractions obey Benford’s Law?

“…His studies resulted in him stating that it would not hold for conventional sets of numbers, such as atomic weights and specific heats of compounds and materials, as his distributions showed, but it was a good fit * E-mail: ep14btech11001@iith.ac.in † E-mail: shantanud@iith.ac.in for quantities such as the numerals from the front pages of newspapers. Over the following years, the distribution has garnered a considerable amount of interest from a variety of specialists, from an assortment of fields, such as biology [5,6], finance [7,8], geophysics [9], seismology [10], spectroscopy [11,12] and astrophysics [13][14][15]. This law also has been used for practical applications in detecting banking frauds [8].…”