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A new three-parameter extension of the log-logistic distribution with applications to survival data

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  • Mohammed K. Shakhatreh

Abstract

In this article, a new three-parameter extension of the two-parameter log-logistic distribution is introduced. Several distributional properties such as moment-generating function, quantile function, mean residual lifetime, the Renyi and Shanon entropies, and order statistics are considered. The estimation of the model parameters for complete and right-censored cases is investigated competently by maximum likelihood estimation (MLE). A simulation study is conducted to show that these MLEs are consistent in moderate samples. Two real datasets are considered; one is a right-censored data to show that the proposed model has a superior performance over several existing popular models.

Suggested Citation

  • Mohammed K. Shakhatreh, 2018. "A new three-parameter extension of the log-logistic distribution with applications to survival data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5205-5226, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:21:p:5205-5226
    DOI: 10.1080/03610926.2017.1388399
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    Cited by:

    1. Isidro Jesús González-Hernández & Luis Carlos Méndez-González & Rafael Granillo-Macías & José Luis Rodríguez-Muñoz & José Sergio Pacheco-Cedeño, 2024. "A New Generalization of the Uniform Distribution: Properties and Applications to Lifetime Data," Mathematics, MDPI, vol. 12(15), pages 1-26, July.
    2. Zawar Hussain & Muhammad Aslam & Zahid Asghar, 2019. "On Exponential Negative-Binomial-X Family of Distributions," Annals of Data Science, Springer, vol. 6(4), pages 651-672, December.
    3. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.
    4. Abdisalam Hassan Muse & Samuel M. Mwalili & Oscar Ngesa, 2021. "On the Log-Logistic Distribution and Its Generalizations: A Survey," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(3), pages 1-93, June.

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