  Global observables such as the pseudorapidity distributions of particle
multiplicities in the final state are crucial to shed light into the physics
processes involved in hadronic collisions. In proton$-$lead (p$-$Pb) collisions
at Large Hadron Collider (LHC) energies, such measurements provide an important
baseline to understand lead$-$lead (Pb$-$Pb) results by disentangling hot
nuclear matter effects from the ones due to the cold nuclear matter.
Multiplicity measurements can also put constraints on theoretical models
describing the initial stages of the collision, e.g., to what degree the
nucleon and the nuclei interact as dilute (partons) or dense (CGC-like) fields.
The study of inclusive photon multiplicity aims to provide complementary
measurements to those obtained with charged particles.
  In these proceedings, the pseudorapidity distributions of inclusive photons
at forward pseudorapidity ($2.3 < \eta_{\rm lab} < 3.9$) in pp and p$-$Pb
collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV are presented. The data samples
were collected using the Photon Multiplicity Detector (PMD) of ALICE. The
multiplicity dependence of photon production in p$-$Pb collisions is presented
and a comparison with charged-particle distributions measured at
mid-pseudorapidity is shown. The results are also compared with predictions
from Monte Carlo event generators.
