  We utilize click-counting theory for the reconstruction of photon statistics.
Our approach employs an analytic pseudo-inversion method to estimate photon
counts from measured click counts. A reconfigurable time-bin multiplexing,
click-counting detector is set up that renders it possible to alter the
photon-number resolution as needed. A detector tomography is carried out,
yielding vital measurement features, such as quantum efficiencies, cross-talk
rates, etc. We gauge the success of the pseudo-inversion by applying the Mandel
and binomial parameters, resulting in an additional interpretation of these
parameters for the discrimination of distinct quantum statistics. In addition,
we apply a loss deconvolution technique to account for detection losses.
