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The linearly decreasing stress Weibull (LDSWeibull): a new Weibull-like distribution

Author

Listed:
  • Roger W. Barnard

    (Texas Tech University, Department of Mathematics & Statistics)

  • Chamila Perera

    (Texas Tech University, Department of Mathematics & Statistics)

  • James G. Surles

    (Texas Tech University, Department of Mathematics & Statistics)

  • A. Alexandre Trindade

    (Texas Tech University, Department of Mathematics & Statistics)

Abstract

Motivated by an engineering pullout test applied to a steel strip embedded in earth, we show how the resulting linearly decreasing force leads naturally to a new distribution, if the force under constant stress is modeled via a three-parameter Weibull. We term this the LDSWeibull distribution, and show that inference on the parameters of the underlying Weibull can be made upon collection of data from such pullout tests. Various classical finite-sample and asymptotic properties of the LDSWeibull are studied, including existence of moments, distribution of extremes, and maximum likelihood based inference under different regimes. The LDSWeibull is shown to have many similarities with the Weibull, but does not suffer from the problem of having an unbounded likelihood function under certain parameter configurations. We demonstrate that the quality of its fit can also be very competitive with that of the Weibull in certain applications.

Suggested Citation

  • Roger W. Barnard & Chamila Perera & James G. Surles & A. Alexandre Trindade, 2019. "The linearly decreasing stress Weibull (LDSWeibull): a new Weibull-like distribution," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-21, December.
    • Handle: RePEc:spr:jstada:v:6:y:2019:i:1:d:10.1186_s40488-019-0100-8
    DOI: 10.1186/s40488-019-0100-8
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