  Photon number resolving detectors can be highly useful for studying the
statistics of multi-photon quantum states of light. In this work we study the
counts statistics of different states of light measured on multiplexed on-off
detectors. We put special emphasis on artificial nonclassical features of the
statistics obtained. We show new ways to derive analytical formulas for counts
statistics and their moments. Using our approach we are the first to derive
statistics moments for multi-mode thermal states measured on multiplexed on-off
detectors. We use them to determine empirical Mandel parameters and recently
proposed subbinomial parameters suitable for tests of nonclassicality of the
measured states. Additionally, we investigate subpoissonian and superbunching
properties of the two-mode squeezed state measured on a pair of multiplexed
detectors and we present results of the Fano factor and second-order
correlation function for these states.
