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