Generalized Boltzmann factors induced by Weibull-type distributions

The inverse Mellin transform technique is utilized to obtain closed form representations of the generalized Boltzmann factors associated with several Weibull-type models such as the generalized gamma, Maxwell, Rayleigh and half-normal distributions. The results complement those already available in the Physics literature in connection with the distribution of certain variables affecting the behavior of nonequilibrium systems subject to complex dynamics, which include for instance computable expressions for the generalized Boltzmann factors induced by the gamma, F, uniform and lognormal statistical models.