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The odd log-logistic logarithmic generated family of distributions with applications in different areas

Author

Listed:
  • Morad Alizadeh

    (Persian Gulf university)

  • S. M. T. K. MirMostafee

    (University of Mazandaran)

  • Edwin M. M. Ortega

    (Universidade de São Paulo)

  • Thiago G. Ramires

    (Universidade de São Paulo)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco)

Abstract

We introduce and study general mathematical properties of a new generator of continuous distributions with three extra parameters called the odd log-logistic logarithmic generated family of distributions. We present some special models and investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Shannon and Rényi entropies and order statistics, which hold for any baseline model, are determined. We discuss the estimation of the model parameters by maximum likelihood. Further, we introduce the new family in long-term survival models. We illustrate the potentiality of the proposed models by means of four applications to real data.

Suggested Citation

  • Morad Alizadeh & S. M. T. K. MirMostafee & Edwin M. M. Ortega & Thiago G. Ramires & Gauss M. Cordeiro, 2017. "The odd log-logistic logarithmic generated family of distributions with applications in different areas," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0062-7
    DOI: 10.1186/s40488-017-0062-7
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    References listed on IDEAS

    as
    1. Gauss Cordeiro & Saralees Nadarajah & Edwin Ortega, 2012. "The Kumaraswamy Gumbel distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 139-168, June.
    2. Elizabeth Hashimoto & Gauss Cordeiro & Edwin Ortega, 2013. "The new Neyman type A beta Weibull model with long-term survivors," Computational Statistics, Springer, vol. 28(3), pages 933-954, June.
    3. Edwin M.M. Ortega & Gauss M. Cordeiro & Michael W. Kattan, 2012. "The negative binomial--beta Weibull regression model to predict the cure of prostate cancer," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1191-1210, November.
    4. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
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    Cited by:

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    2. Lucas David Ribeiro-Reis, 2023. "The Log-Logistic Regression Model Under Censoring Scheme," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-12, June.

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