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The logistic-X family of distributions and its applications

Author

Listed:
  • M. H. Tahir
  • Gauss M. Cordeiro
  • Ayman Alzaatreh
  • M. Mansoor
  • M. Zubair

Abstract

The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its density function can be symmetrical, left-skewed, right-skewed, and reversed-J shaped, and can have increasing, decreasing, bathtub, and upside-down bathtub hazard rates shaped. Further, it can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon entropy, and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. We also investigate the properties of one special model, the logistic-Fréchet distribution, and illustrate its importance by means of two applications to real data sets.

Suggested Citation

  • M. H. Tahir & Gauss M. Cordeiro & Ayman Alzaatreh & M. Mansoor & M. Zubair, 2016. "The logistic-X family of distributions and its applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(24), pages 7326-7349, December.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:24:p:7326-7349
    DOI: 10.1080/03610926.2014.980516
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    Citations

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    Cited by:

    1. Peña-Ramírez, Fernando A. & Guerra, Renata Rojas & Canterle, Diego Ramos & Cordeiro, Gauss M., 2020. "The logistic Nadarajah–Haghighi distribution and its associated regression model for reliability applications," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    2. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    3. Joseph Thomas Eghwerido & Pelumi E. Oguntunde & Friday Ikechukwu Agu, 2023. "The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 172-197, February.
    4. Aliyu Ismail Ishaq & Alfred Adewole Abiodun, 2020. "The Maxwell–Weibull Distribution in Modeling Lifetime Datasets," Annals of Data Science, Springer, vol. 7(4), pages 639-662, December.
    5. Haitham M. Yousof & Mustafa Ç. Korkmaz & Subhradev Sen, 2021. "A New Two-Parameter Lifetime Model," Annals of Data Science, Springer, vol. 8(1), pages 91-106, March.
    6. Alya Al Mutairi & Muhammad Z. Arshad, 2022. "A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(2), pages 1-29, March.
    7. Fiaz Ahmad Bhatti & G. G. Hamedani & Mustafa C. Korkmaz & Gauss M. Cordeiro & Haitham M. Yousof & Munir Ahmad, 2019. "On Burr III Marshal Olkin family: development, properties, characterizations and applications," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-21, December.
    8. Tommaso Lando & Lucio Bertoli-Barsotti, 2020. "Stochastic dominance relations for generalised parametric distributions obtained through composition," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 297-311, December.
    9. Showkat Ahmad Lone & Tabassum Naz Sindhu & Marwa K. H. Hassan & Tahani A. Abushal & Sadia Anwar & Anum Shafiq, 2023. "Theoretical Structure and Applications of a Newly Enhanced Gumbel Type II Model," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    10. 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.
    11. Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    12. Marganpoor Shahdie & Ranjbar Vahid & Alizadeh Morad & Abdollahnezhad Kamel, 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.
    13. Aryal Gokarna R. & Yousof Haitham M., 2017. "The Exponentiated Generalized-G Poisson Family of Distributions," Stochastics and Quality Control, De Gruyter, vol. 32(1), pages 7-23, June.
    14. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.

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