The Break-By-One Gamma Distribution: A Proper and Tractable Alternative to the Schechter Function for Modeling Cosmic Populations

TL;DR

The paper introduces the break-by-one gamma distribution as a proper, normalizable alternative to the Schechter function for modeling cosmic populations, with easy sampling due to its gamma connection.

Contribution

It proposes a new distribution that addresses the non-normalizability of the Schechter function and is straightforward to sample from, enhancing cosmic demographic modeling.

Findings

Proper and normalizable alternative to Schechter function

Easy sampling due to gamma distribution connection

Applicable to cosmic population modeling

Abstract

The break-by-one gamma distribution has a probability density function resembling the Schechter function, but with the small-argument behavior modified so it is normalizable in commonly arising cases where the Schechter function is not. Its connection to the gamma distribution makes it straightforward to sample from. These properties make it useful for cosmic demographics.