  Astrophysical sources of TeV gamma rays are usually established by Cherenkov
telescope observations. These counting type instruments have a field of view of
few degrees in diameter and record large numbers of particle air showers via
their Cherenkov radiation in the atmosphere. The showers are either induced by
gamma rays or diffuse cosmic ray background. The commonly used test statistic
to evaluate a possible gamma-ray excess is Li and Ma (1983), Eq. 17, which can
be applied to independent on- and off-source observations, or scenarios that
can be approximated as such. This formula however is unsuitable if the data are
taken in so-called "wobble" mode (pointing to several offset positions around
the source), if at the same time the acceptance shape is irregular or even
depends on operating parameters such as the pointing direction or telescope
multiplicity. To provide a robust test statistic in such cases, this paper
explores a possible generalization of the likelihood ratio concept on which the
formula of Li and Ma is based. In doing so, the multi-pointing nature of the
data and the typically known instrument point spread function are fully
exploited to derive a new, semi-numerical test statistic. Due to its
flexibility and robustness against systematic uncertainties, it is not only
useful for detection purposes, but also for skymapping and source shape
fitting. Simplified Monte Carlo simulations are presented to verify the
results, and several applications and further generalizations of the concept
are discussed.
