  The light curves observed from X-ray pulsars and magnetars reflect the
radiation emission pattern, the geometry of the magnetic field, and the neutron
star compactness. We study the statistics of X-ray pulse profiles in order to
constrain the neutron star compactness and the magnetic field geometry. We
collect the data for 124 X-ray pulsars, which are mainly in high-mass X-ray
binary systems, and classify their pulse profiles according to the number of
observed peaks seen during one spin period, dividing them into two classes,
single- and double-peaked. We find that the pulsars are distributed about
equally between both groups. We also compute the probabilities predicted by the
theoretical models of two antipodal point-like spots that emit radiation
according to the pencil-like emission patterns. These are then compared to the
observed fraction of pulsars in the two classes. Assuming a blackbody emission
pattern, it is possible to constrain the neutron star compactness if the
magnetic dipole has arbitrary inclinations to the pulsar rotational axis. More
realistic pencil-beam patterns predict that 79% of the pulsars are
double-peaked independently of their compactness. The theoretical predictions
can be made consistent with the data if the magnetic dipole inclination to the
rotational axis has an upper limit of 40+/-4 deg. We also discuss the effect of
limited sensitivity of the X-ray instruments to detect weak pulses, which
lowers the number of detected double-peaked profiles and makes the theoretical
predictions to be consistent with the data even if the magnetic dipole does
have random inclinations. This shows that the statistics of pulse profiles does
not allow us to constrain the neutron star compactness. In contrast to the
previous claims by Bulik et al. (2003), the data also do not require the
magnetic inclination to be confined in a narrow interval.
