On the [formula omitted]-type distributions

Abstract

Various q-type distributions have appeared in the physics literature in the recent years, see e.g. L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q -exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q -exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678–688. A.M.C. de Souza, C. Tsallis, Student's t - and r - distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52–57. It is pointed out in the paper that many of these are the same as or particular cases of what has been known in the statistics literature. Several of these statistical distributions are discussed and references provided. We feel that this paper could be of assistance for modeling problems of the type considered by L.C. Malacarne, R.S. Mendes, E. K. Lenzi, q -exponential distribution in urban agglomeration, Phys. Rev. E 65, (2002) 017106. S.M.D. Queiros, On a possible dynamical scenario leading to a generalised Gamma distribution, in xxx.lanl.gov-physics/0411111. U.M.S. Costa, V.N. Freire, L.C. Malacarne, R.S. Mendes, S. Picoli Jr., E.A. de Vasconcelos, E.F. da Silva Jr., An improved description of the dielectric breakdown in oxides based on a generalized Weibull distribution, Physica A 361, (2006) 215. S. Picoli, Jr., R.S. Mendes, L.C. Malacarne, q -exponential, Weibull, and q-Weibull distributions: an empirical analysis, Physica A 324 (2003) 678–688. A.M.C. de Souza, C. Tsallis, Student's t - and r - distributions: unified derivation from an entropic variational principle, Physica A 236 (1997) 52–57 and others.