This paper estimates the generalized and nested models with SGED and skewed t distributions to determine the correct specification of the conditional distribution of short-term interest rates. First, the paper generalized the parametric models of short-term interest rate that nest one-factor CEV model with linear drift and level effect. Second, the paper nested the discrete-time GARCH models that incorporate the level and GARCH effects into the diffusion function. The empirical research points out that the significant parametric estimate reduces the level effect for the variance function. Moreover, the results can not fully capture modeling the dynamics of short-term interest rate volatility that only with level effect. Finally, the results also show that the significance of nonlinearity in the drift function relies crucially on the specification of the volatility function.