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Compounded Inverse Weibull Distributions: Properties, Inference and Applications

Author

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  • Jimut Bahan Chakrabarty

    (Indian Institute of Management Kozhikode)

  • Shovan Chowdhury

    (Indian Institute of Management Kozhikode)

Abstract

In this paper two probability distributions are introduced compounding inverse Weibull distribution with Poisson and geometric distributions. The distributions can be used to model lifetime of series system where the lifetimes follow inverse Weibull distribution and the subgroup size being random follows either geometric or Poisson distribution. Some of the important statistical and reliability properties of each of the distributions are derived. The distributions are found to exhibit both monotone and non-monotone failure rates. The parameters of the distributions are estimated using the maximum likelihood method and the expectation-maximization algorithm. The potentials of the distributions are explored through three real life data sets and are compared with similar compounded distributions, viz. Weibull-geometric, Weibull-Poisson, exponential-geometric and exponential-Poisson distributions.

Suggested Citation

  • Jimut Bahan Chakrabarty & Shovan Chowdhury, 2016. "Compounded Inverse Weibull Distributions: Properties, Inference and Applications," Working papers 213, Indian Institute of Management Kozhikode.
    • Handle: RePEc:iik:wpaper:213
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    References listed on IDEAS

    as
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    2. Chahkandi, M. & Ganjali, M., 2009. "On some lifetime distributions with decreasing failure rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4433-4440, October.
    3. Ali Akbar Bromideh, 2012. "Discriminating Between Weibull and Log-Normal Distributions Based on Kullback-Leibler Divergence," Istanbul University Econometrics and Statistics e-Journal, Department of Econometrics, Faculty of Economics, Istanbul University, vol. 16(1), pages 44-54, May.
    4. 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.
    5. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
    6. Morais, Alice Lemos & Barreto-Souza, Wagner, 2011. "A compound class of Weibull and power series distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1410-1425, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Inverse Weibull distribution; Poisson distribution; Geometric distribution; Hazard function; Maximum likelihood estimation; EM algorithm.;
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