A recommended procedure for estimating the cosmic-ray spectral parameter of a simple power law

A simple power law model with single spectral index α1 is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 1013 eV. Two procedures for estimating α1--the method of moments and maximum likelihood (ML)--are developed and their statistical performance are compared. The ML procedure is shown to be the superior approach and is then generalized for application to real cosmic-ray data sets. Several other important results, such as the relationship between collecting power and detector energy resolution and inclusion of a non-Gaussian detector response function, are presented. These results have many practical benefits in the design phase of a cosmic-ray detector as they permit instrument developers to make important trade studies in design parameters as a function of one of the science objectives