Smooth recurrent estimation of multivariate reliability function

Empirical distribution and reliability functions are discrete that often does not correspond to real random variables in technical and physical applications. Smooth recurrent nonparametric estimators of the multivariate reliability function based on the product of the Laplace kernel functions are suggested. The asymptotic mean square error (MSE) of the estimator and its limiting distribution are presented that allow a new recurrent interval estimator of the reliability function to be constructed. Advantages of the suggested recurrent estimators over the well-known parametric algorithms are discussed.