New Probability Distributions in Astrophysics: VII. The Truncated Gamma-Pareto Distribution Applied to Cosmic Rays

Abstract

Many astrophysical phenomena are modeled by an inverse power law distribution at high values of the random variable but often at low values of the random variable we have a departure from an inverse power law. In order to insert a continuous transition from low to high values of the random variable we analyse the truncated gamma-Pareto distribution in two versions by deriving the most important statistical parameters. The application of the results to the distribution in energy of cosmic rays allows deriving an analytical expression for the average energy, which is 2.6 GeV.