It is widely known that the switching time is determined by the thermal stability parameters and external perturbations such as magnetic field and/or spin polarized current in magnetic nano-structures. Since the thermal stability parameter and switching time are crucial values in the design of spin-transfer torque magnetic random access memory, the measurement of the switching time is important in the study of the switching behavior of ferromagnetic nano-structures. In this study, we focus on the distribution of the switching time. Within the limit of a large energy barrier, a simple analytical expression between damping constant and anisotropy field with switching time distribution is obtained and confirmed by numerically solving the Fokker-Planck equation. We show that the damping constant and anisotropy field can be extracted by measuring the full width half maximum of the switching time distribution in the magnetic nano-structure devices. Furthermore, the present method can be applied to not only single nano-structure, but also inhomogeneous nano-structure arrays.