Gamma and Reciprocal Inverse Gaussian Kernel Estimators for Stress Strength Reliability Model

Abstract

Several parametric estimation methods have been applied to estimate the reliability of a stress strength model. In this paper, we focus on the nonparametric kernel method and propose two nonparametric estimators based, respectively, on the Gamma and Reciprocal Inverse Gaussian kernels, which are nonnegative kernels, free from boundary bias and achieve the optimal rate of convergence for the mean integrated squared error. We introduce reliability estimators and establish their statistical and asymptotic properties, namely: bias, variance, and mean square error. We also study the selection of the smoothing parameter using the rule-of-thumb and unbiased cross-validation approaches, since it plays an important role in kernel estimation. Finally, a simulation study and an application to real data are carried out to highlight the performance of the proposed estimators.