Over the last century, the overdensities in the velocity distributions of nearby stars were attributed to stellar kinematic groups or moving groups. Although their reality was initially questioned, their existence is now supported by a confluence of evidence. To pursue investigations, quantitative methods should be clearly defined to identify new stars belonging to these groups. Here, we present two probabilistic methods to determine the likelihood of kinematic membership for possible candidates in five of the known young stellar kinematic groups - namely, Pleiades, IC2391, Castor, Ursa Major, and Hyades - in which all are younger than 650Myr. We tried different methods to handle kinematic data of their known members. We succeeded in developing two independent procedures able to identify new candidates of these five stellar stream. We tested the robustness of our two approaches by means of extensive Monte Carlo simulations. Our methods are consistent with one another in more than 90% of cases and for almost all the stellar kinematic groups under scrutiny. The IC2391 supercluster is an exception. Applying our statistical methods to a large sample of young low-mass stars, we confirmed almost all the likely members and good candidates of these stellar streams. We also proposed 39 additional candidates based on the agreement and the high likelihood of age and kinematic membership. These probabilistic methods are very powerful to reliably identify new candidate members of young stellar kinematic groups. However, the kinematic criteria alone are not sufficient to distinguish between coeval stars that are evaporated from open clusters and other field stars trapped by dynamical processes generated by galactic perturbations. The identification of stars belonging to the remnant of a past star-forming event can be possible with the help of additional information, such as indicators of chromospheric activity, age proxies (lithium abundance), and chemical composition.