## The meteor masses detected by RAMBo and the Newcomb-Bedford law

By Lorenzo Barbieri, Gaetano Brando, Giuseppe Allocca, Fabio Balboni and Daniele Cifiello The Newcomb-Bedford law describes a very strange behavior for “natural” data distributions: looking at the first significant digit if that is not random but follows a logarithmic behavior. We have examined if the meteors mass index measured by RAMBo follows this law and what it means about our data. 1 Introduction Mathematics has sometimes extraordinary mysterious or difficult explanations that make it one of the most fascinating sciences. One of these is the Newcomb-Bedford’s law. The Newcomb-Bedford law, or Newcomb-Bedford distribution, also known as Benford‘s law or law of the first digit, examines numerical data collections from physical measurements. This law does not have an intuitive explanation and at a first glance seems to come rather from the esoteric world than from the statistics world. Let’s see what it is. 2 Newcomb-Bedford law If we extract the first significant digit in each number from a numerical data distribution, we will get a distribution of numbers ranging from 1 to 9. Table 1 shows an example. Table 1 – Example with a distribution of numbers. Number First significant digit 54 5 38 3 361 3 753 7 17 1 76 7 40 4 118 1 521 5 161 1 16749 1 51 5 13 1 74 7 One would expect from this distribution that the probability to find any of the possible significant first digits...

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