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A generalization to the log-inverse Weibull distribution and its applications in cancer research

Author

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  • C. Satheesh Kumar

    (University of Kerala)

  • Subha R. Nair

    (HHMSPB NSS College for Women, University of Kerala)

Abstract

In this paper we consider a generalization of a log-transformed version of the inverse Weibull distribution. Several theoretical properties of the distribution are studied in detail including expressions for its probability density function, reliability function, hazard rate function, quantile function, characteristic function, raw moments, percentile measures, entropy measures, median, mode etc. Certain structural properties of the distribution along with expressions for reliability measures as well as the distribution and moments of order statistics are obtained. Also we discuss the maximum likelihood estimation of the parameters of the proposed distribution and illustrate the usefulness of the model through real life examples. In addition, the asymptotic behaviour of the maximum likelihood estimators are examined with the help of simulated data sets.

Suggested Citation

  • C. Satheesh Kumar & Subha R. Nair, 2021. "A generalization to the log-inverse Weibull distribution and its applications in cancer research," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-30, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00116-1
    DOI: 10.1186/s40488-021-00116-1
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    References listed on IDEAS

    as
    1. Felipe Gusmão & Edwin Ortega & Gauss Cordeiro, 2011. "The generalized inverse Weibull distribution," Statistical Papers, Springer, vol. 52(3), pages 591-619, August.
    2. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    3. Satheesh C. Kumar & Subha R. Nair, 2016. "An extended version of Kumaraswamy inverse Weibull distribution and its properties," Statistica, Department of Statistics, University of Bologna, vol. 76(3), pages 249-272.
    4. Elbatal I., 2011. "Exponentiated Modified Weibull Distribution," Stochastics and Quality Control, De Gruyter, vol. 26(2), pages 189-200, January.
    5. Zhang, Tieling & Xie, Min, 2011. "On the upper truncated Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 194-200.
    6. Ibrahim Elbatal & Francesca Condino & Filippo Domma, 2016. "Reflected Generalized Beta Inverse Weibull Distribution: definition and properties," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 316-340, November.
    7. Mahmoud Aldeni & Carl Lee & Felix Famoye, 2017. "Families of distributions arising from the quantile of generalized lambda distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-18, December.
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