"Influence Method". Detailed mathematical description

A new method for the absolute determination of nuclear particle flux in the absence of known detector efficiency, the "Influence Method", was recently published (I.J. Rios and R.E. Mayer, Nuclear Instruments & Methods in Physics Research A 775 (2015) 99–104). The method defines an estimator for the population and another estimator for the efficiency. In this article we present a detailed mathematical description which yields the conditions for its application, the probability distributions of the estimators and their characteristic parameters. An analysis of the different cases leads to expressions of the estimators and their uncertainties. - Highlights: • "Influence Method", a new method for absolute particle flux determination. • Absolute counting method when detector efficiencies are not known. • Absolute detector efficiency determination