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Generalized Modified Inverse Weibull Distribution: Its Properties and Applications

Author

Listed:
  • Hadi Saboori

    (University of Zabol)

  • Ghobad Barmalzan

    (University of Zabol)

  • Seyyed Masih Ayat

    (University of Zabol)

Abstract

In this paper, we introduce a new useful continuous distribution called generalized modified inverse Weibull distribution. This distribution is a four-parameter extension of the modified inverse Weibull which generalizes some well-known distributions. Various statistical and probabilistic properties are derived such as rth moment, moment generating function, Renyi and Shannon entropies and hazard rate function. We also discuss estimation of the parameters by maximum likelihood and provide the information matrix. The likelihood ratio order (which implies the hazard rate and usual stochastic orders) between smallest order statistics from two independent heterogeneous samples of this new family are discussed. Finally, a real numerical example is also considered for illustrative purposes.

Suggested Citation

  • Hadi Saboori & Ghobad Barmalzan & Seyyed Masih Ayat, 2020. "Generalized Modified Inverse Weibull Distribution: Its Properties and Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 247-269, November.
    • Handle: RePEc:spr:sankhb:v:82:y:2020:i:2:d:10.1007_s13571-018-0182-1
    DOI: 10.1007/s13571-018-0182-1
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    References listed on IDEAS

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    1. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2007. "A flexible Weibull extension," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 719-726.
    2. Carrasco, Jalmar M.F. & Ortega, Edwin M.M. & Cordeiro, Gauss M., 2008. "A generalized modified Weibull distribution for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 450-462, December.
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    Cited by:

    1. Katarína Draganová & Karol Semrád & Monika Blišťanová & Tomáš Musil & Rastislav Jurč, 2021. "Influence of Disinfectants on Airport Conveyor Belts," Sustainability, MDPI, vol. 13(19), pages 1-13, September.
    2. Haiping Ren & Xue Hu, 2023. "Bayesian Estimations of Shannon Entropy and Rényi Entropy of Inverse Weibull Distribution," Mathematics, MDPI, vol. 11(11), pages 1-16, May.

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