To check the validity of an assumed parametric model for failure time data, we compare the generalized Kaplan-Meier estimator Fn(t) of a distribution function with the estimated distribution function under the assumed model, where is the maximum likelihood estimator. The generalized parametric empirical process is approximated by the stochastic integrals with respect to a martingale. It converges in distribution to a Gaussian process which can be represented by stochastic integrals with respect to a Wiener process. The weak convergence of parametric empirical process on the whole line is derived for random right censored and/or left truncated data. Through the transformation of the limit Gaussian process to a Guassian martingale, we obtain a class of goodness-of-fit tests for the parametric model.