Improved Methods of Hazard Rate Function Calculation Using Saddlepoint Approximations

In this study, we improve a saddlepoint approximation technique for calculating the hazard rate function for some complicated models such as the stopped sum of random variables. Saddlepoint approximations for the computation of survival and hazard functions are presented in parametric survival analysis. Although these approximation methods are very accurate, save time and effort, their use in hazard rate calculations has been ignored. In this study, we estimate the hazard rate function based on the Lugannani and Rice saddlepoint approximation to derive the saddlepoint density and the mass function for these complicated models. Numerical applications are provided to confirm the performance of this technique.