TY  - JOUR
AU  - Ding, Juan
AU  - Zhou, Chi
AU  - Xia, Anqi
AU  - Zhou, Wenxin
AU  - Xiong, Wenjun
PY  - 2026
TI  - A two-parameter family of Hollander–Proschan–type tests against NBUE alternatives
JO  - AIMS Mathematics
SP  - 13567
EP  - 13588
VL  - 11
IS  - 5
AB  - 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.
UR  - https://doi.org/10.3934/math.2026558
DO  - 10.3934/math.2026558