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Pulsars' gamma-ray luminosities are thought to exceed their radioluminosities by several orders of magnitude: a notion that is based on theassumption that the decay with distance of the flux of gamma-ray pulses obeysthe inverse-square law as does that of the flux of radio pulses. However,results of testing the hypothesis of independence of luminosities and distancesof gamma-ray pulsars by means of the Efron--Petrosian statistic imply that theobservational data in the second {\it FERMI} catalogue are consistent with thedependence $S\propto D^{-3/2}$ of the flux densities $S$ of these pulsars ontheir distances $D$ at substantially higher levels of significance than theyare with the dependence $S\propto D^{-2}$. This is not incompatible with therequirements of the conservation of energy because the radiation processdescribed in Ardavan [{\it Mon. Not. R. Astron. Soc.}, {\bf 507}, 4530--4563(2021)], by which the superluminally moving current sheet in the magnetosphereof a neutron star is shown to generate the observed gamma-ray pulses, isintrinsically transient: the difference in the fluxes of power across any twospheres centred on the star is balanced by the change with time of the energycontained inside the shell bounded by those spheres. Once the over-estimationof their values is rectified, the luminosities of gamma-ray pulsars turn out tohave the same range of values as do the luminosities of radio pulsars.

Dependence of the flux of gamma-ray pulsars on distance: A nonparametric analysis of the data in the second FERMI catalogue