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This paper proposes the nonparametric kernel method for the hazard rate (HR) function estimation in the context of positively skewed data. The class of generalized Birnbaum-Saunders (GBS) kernels is considered because of its several interesting properties and flexibility. Some asymptotic properties, such as bias, variance and mean integrated squared error (MISE) are established for the proposed estimator. In addition, we demonstrate that, the GBS-HR estimator is strongly consistent and asymptotically normal. The choice of bandwidth is also investigated by rule of thumb and unbiased cross validation approaches. Finally, performances of the HR estimator based on GBS kernels and comparison of the two bandwidth selection methods are illustrated by a simulation study and real applications.

Generalized Birnbaum–Saunders kernel for hazard rate function estimation