Nonparametric inference for NBUE distributions based on the TTT transform

Abstract

This paper presents a uniformly consistent estimator for the cumulative distribution function, operating under the assumption of “new better than used in expectation” (NBUE). Additionally, it introduces a novel class of consistent tests for the NBUE null hypothesis. Both procedures leverage the empirical total time on test (TTT) transform. Finite sample properties of the proposed methods are investigated through simulations.