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A new compounding life distribution: the Weibull--Poisson distribution

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  • Wanbo Lu
  • Daimin Shi

Abstract

In this paper, a new compounding distribution, named the Weibull--Poisson distribution is introduced. The shape of failure rate function of the new compounding distribution is flexible, it can be decreasing, increasing, upside-down bathtub-shaped or unimodal. A comprehensive mathematical treatment of the proposed distribution and expressions of its density, cumulative distribution function, survival function, failure rate function, the k th raw moment and quantiles are provided. Maximum likelihood method using EM algorithm is developed for parameter estimation. Asymptotic properties of the maximum likelihood estimates are discussed, and intensive simulation studies are conducted for evaluating the performance of parameter estimation. The use of the proposed distribution is illustrated with examples.

Suggested Citation

  • Wanbo Lu & Daimin Shi, 2012. "A new compounding life distribution: the Weibull--Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 21-38, March.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:1:p:21-38
    DOI: 10.1080/02664763.2011.575126
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    References listed on IDEAS

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    1. Barreto-Souza, Wagner & Cribari-Neto, Francisco, 2009. "A generalization of the exponential-Poisson distribution," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2493-2500, December.
    2. David Hinkley, 1977. "On Quick Choice of Power Transformation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(1), pages 67-69, March.
    3. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
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    Cited by:

    1. Almalki, Saad J. & Nadarajah, Saralees, 2014. "Modifications of the Weibull distribution: A review," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 32-55.
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    3. Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    4. Min Wang & Ibrahim Elbatal, 2015. "The modified Weibull geometric distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 303-315, December.
    5. Ahmed Elshahhat & EL-Sayed A. El-Sherpieny & Amal S. Hassan, 2023. "The Pareto–Poisson Distribution: Characteristics, Estimations and Engineering Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1058-1099, February.
    6. Eryilmaz, Serkan, 2016. "A new class of lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 63-71.
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