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The objective of the Karlsruhe Tritium Neutrino (KATRIN) experiment is todetermine the effective electron neutrino mass $m(\nu_\text{e})$ with anunprecedented sensitivity of $0.2\,\text{eV}$ (90\% C.L.) by precision electronspectroscopy close to the endpoint of the $\beta$ decay of tritium. We presenta consistent theoretical description of the $\beta$ electron energy spectrum inthe endpoint region, an accurate model of the apparatus response function, andthe statistical approaches suited to interpret and analyze tritium $\beta$decay data observed with KATRIN with the envisaged precision. In addition toproviding detailed analytical expressions for all formulae used in thepresented model framework with the necessary detail of derivation, we discussand quantify the impact of theoretical and experimental corrections on themeasured $m(\nu_\text{e})$. Finally, we outline the statistical methods forparameter inference and the construction of confidence intervals that areappropriate for a neutrino mass measurement with KATRIN. In this context, webriefly discuss the choice of the $\beta$ energy analysis interval and thedistribution of measuring time within that range.

$\beta$-Decay Spectrum, Response Function and Statistical Model for Neutrino Mass Measurements with the KATRIN Experiment