@article{Ding2026, 
author = {Juan Ding and Chi Zhou and Anqi Xia and Wenxin Zhou and Wenjun Xiong},
title = {A two-parameter family of Hollander–Proschan–type tests against NBUE alternatives},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {13567-13588},
keywords = {NBUE, Hollander–Proschan test, Pitman asymptotic efficiency, reliability, mean residual life},
url = {https://www.sciopen.com/article/10.3934/math.2026558},
doi = {10.3934/math.2026558},
abstract = {Testing for aging behavior is a fundamental problem in reliability analysis. We study tests of exponentiality against new better than used in expectation (NBUE) alternatives. Many Hollander–Proschan type procedures can be interpreted as weighted functionals of a common mean residual life gap, but are often presented in isolated forms, making it difficult to understand how weighting affects sensitivity to different alternatives. We develop a unified weighted-functional framework in which several classical procedures arise as special or limiting cases. Within this framework, we construct a centered and studentized statistic with an asymptotic normal null distribution and an explicit centering term. Pitman efficiency analysis and Monte Carlo experiments illustrate how weighting influences sensitivity and finite-sample performance, while real-data applications demonstrate practical interpretability.}
}