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A new generalized odd log-logistic family of distributions

Author

Listed:
  • Hossein Haghbin
  • Gamze Ozel
  • Morad Alizadeh
  • G. G. Hamedani

Abstract

We introduce and study general mathematical properties of a new generator of continuous distributions with three extra parameters called the new generalized odd log-logistic family of distributions. The proposed family contains several important classes discussed in the literature as submodels such as the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, entropy measures, and order statistics, which hold for any baseline model, are presented. We also present certain characterization of the proposed distribution and derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behavior of the maximum likelihood estimator via simulation. The importance of the new family is illustrated by means of two real data sets. These applications indicate that the new family can provide better fits than other well-known classes of distributions. The beauty and importance of the new family lies in its ability to model real data.

Suggested Citation

  • Hossein Haghbin & Gamze Ozel & Morad Alizadeh & G. G. Hamedani, 2017. "A new generalized odd log-logistic family of distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 9897-9920, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:20:p:9897-9920
    DOI: 10.1080/03610926.2016.1222428
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    Cited by:

    1. Emrah Altun & Mustafa Ç. Korkmaz & Mahmoud El-Morshedy & Mohamed S. Eliwa, 2021. "A New Flexible Family of Continuous Distributions: The Additive Odd-G Family," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    2. Shahdie Marganpoor & Vahid Ranjbar & Morad Alizadeh & Kamel Abdollahnezhad, 2020. "Generalised Odd Frechet Family of Distributions: Properties and Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(3), pages 109-128, September.

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