Empirical Mantissa Distributions of Pulsars

TL;DR

This paper investigates the distribution of first digits in pulsar data, finding most conform to Benford's law except for barycentric period, which deviates but follows a generalized version, aiding pulsar modeling.

Contribution

It systematically analyzes mantissa distributions of pulsar quantities, revealing conformity and deviations from Benford's law, and highlights pulsars as a model for studying real-world data digit distributions.

Findings

Most pulsar quantities follow Benford's law.

Barycentric period deviates but fits a generalized Benford's law.

Pulsars can help constrain models of digit distribution in real data.

Abstract

The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's law. Here, we investigate systematically the mantissa distributions of some pulsar quantities, and find that for most quantities their first digits conform to this law. However, the barycentric period shows significant deviation from the usual distribution, but satisfies a generalized Benford's law roughly. Therefore pulsars can serve as an ideal assemblage to study the first digit distributions of real world data, and the observations can be used to constrain theoretical models of pulsar behavior.