  We report measurements of the primary charged particle pseudorapidity density
and transverse momentum distributions in p-Pb collisions at $\sqrt{s_{\rm NN}}$
= 5.02 TeV, and investigate their correlation with experimental observables
sensitive to the centrality of the collision. Centrality classes are defined
using different event activity estimators, i.e. charged particle multiplicities
measured in three disjunct pseudorapidity regions as well as the energy
measured at beam rapidity (zero-degree). The procedures to determine the
centrality, quantified by the number of participants ($N_{\rm part}$), or the
number of nucleon-nucleon binary collisions ($N_{\rm coll}$), are described. We
show that, in contrast to Pb-Pb collisions, in p-Pb collisions large
multiplicity fluctuations together with the small range of participants
available, generate a dynamical bias in centrality classes based on particle
multiplicity. We propose to use the zero-degree energy, which we expect not to
introduce a dynamical bias, as an alternative event-centrality estimator. Based
on zero-degree energy centrality classes, the $N_{\rm part}$ dependence of
particle production is studied. Under the assumption that the multiplicity
measured in the Pb-going rapidity region scales with the number of
Pb-participants, an approximate independence of the multiplicity per
participating nucleon measured at mid-rapitity of the number of participating
nucleons is observed. Furthermore, at high-$p_{\rm T}$ the p-Pb spectra are
found to be consistent with the pp spectra scaled by $N_{\rm coll}$ for all
centrality classes. Our results represent valuable input for the study of the
event activity dependence of hard probes in p-Pb collision and, hence, help to
establish baselines for the interpretation of the Pb-Pb data.
