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Nonparametric inference for NBUE distributions based on the TTT transform

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  • Lando, Tommaso

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.

Suggested Citation

  • Lando, Tommaso, 2024. "Nonparametric inference for NBUE distributions based on the TTT transform," Statistics & Probability Letters, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:stapro:v:212:y:2024:i:c:s0167715224001263
    DOI: 10.1016/j.spl.2024.110157
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    References listed on IDEAS

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    1. Lando, Tommaso, 2023. "Testing departures from the increasing hazard rate property," Statistics & Probability Letters, Elsevier, vol. 193(C).
    2. Richard E. Barlow, 1979. "Geometry of the total time on test transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 393-402, September.
    3. Anis, M.Z. & Mitra, M., 2011. "A generalized Hollander-Proschan type test for NBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 126-132, January.
    4. Kan Cheng & Yeh Lam, 2002. "Reliability bounds for the NBUE distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 781-797, December.
    5. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    6. Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
    7. Rojo, J. & Samaniego, F. J., 1994. "Uniform Strong Consistent Estimation of an Ifra Distribution Function," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 150-163, April.
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