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On nonparametric maximum likelihood estimation of a distribution uniformly stochastically smaller than a standard

Author

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  • Rojo, Javier
  • Samaniego, Francisco J.

Abstract

The class of distributions F which are uniformly stochastically smaller than a known standard G arises naturally when life testing experiments are conducted in an environment more severe or stressful than the environment in which the system has been pretested. The problem of estimating a distribution in this class via nonparametric maximum likelihood is considered. Under the assumption that the standard lifetime distribution G is continuous and strictly increasing, the NPMLE of F is derived in closed form, and its inconsistency is demonstrated.

Suggested Citation

  • Rojo, Javier & Samaniego, Francisco J., 1991. "On nonparametric maximum likelihood estimation of a distribution uniformly stochastically smaller than a standard," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 267-271, March.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:3:p:267-271
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    Cited by:

    1. El Barmi, Hammou & Mukerjee, Hari, 2016. "Consistent estimation of survival functions under uniform stochastic ordering; the k-sample case," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 99-109.
    2. Ori Davidov & George Iliopoulos, 2012. "Estimating a distribution function subject to a stochastic order restriction: a comparative study," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 923-933, December.
    3. Bhaskar Bhattacharya, 1997. "On Tests of Symmetry Against One-Sided Alternatives," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 237-254, June.

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