We found that the rare distribution of velocities in quasisteady states of the dipole-type Hamiltonian mean-field model can be explained by the Cairns-Tsallis distribution, which has been used to describe nonthermal electron populations of some plasmas. This distribution gives us two interesting parameters which allow an adequate interpretation of the output data obtained through molecular dynamics simulations, namely, the characteristic parameter $q$ of the so-called nonextensive systems and the $\alpha$ parameter, which can be seen as an indicator of the number of particles with nonequilibrium behavior in the distribution. Our analysis shows that fit parameters obtained for the dipole-type Hamiltonian mean-field simulated system are ad hoc with some nonthermality and nonextensivity constraints found by different authors for plasma systems described through the Cairns-Tsallis distribution.