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Robust estimators for one-shot device testing data under gamma lifetime model with an application to a tumor toxicological data

Author

Listed:
  • N. Balakrishnan

    (McMaster University)

  • E. Castilla

    (Complutense University of Madrid)

  • N. Martín

    (Complutense University of Madrid)

  • L. Pardo

    (Complutense University of Madrid)

Abstract

Due to its flexibility, gamma distribution is commonly used for lifetime data analysis in reliability and survival studies, and especially in one-shot device testing data. In the study of such data, inducing more failures by accelerated life tests is a common practice, to obtain more lifetime information within a relatively short period of time. In this paper, we develop weighted minimum density power divergence estimators, as a natural extension of the classical maximum likelihood estimator, in the analysis of one-shot device testing data, under accelerated life tests based on gamma lifetime distribution. Wald-type test statistics, based on these estimators, are also developed. Through a Monte Carlo simulation study, the suggested estimators and tests are shown to be robust alternatives to the maximum likelihood estimators and the classical Wald tests based on them. Finally, these procedures are applied to a mice tumor toxicological data for illustrative purpose.

Suggested Citation

  • N. Balakrishnan & E. Castilla & N. Martín & L. Pardo, 2019. "Robust estimators for one-shot device testing data under gamma lifetime model with an application to a tumor toxicological data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 991-1019, November.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:8:d:10.1007_s00184-019-00718-5
    DOI: 10.1007/s00184-019-00718-5
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    References listed on IDEAS

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    1. Balakrishnan, N. & Ling, M.H., 2012. "EM algorithm for one-shot device testing under the exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 502-509.
    2. Balakrishnan, N. & Ling, M.H., 2014. "Gamma lifetimes and one-shot device testing analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 54-64.
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