The Topp–Leone Lomax (TLLo) Distribution with Applications to Airbone Communication Transceiver Dataset

  • Pelumi E. OguntundeEmail author
  • Mundher A. Khaleel
  • Hilary I. Okagbue
  • Oluwole A. Odetunmibi


The Lomax distribution was extended in this paper using the Topp–Leone family of distributions. Some of its specific structural properties were established and the model parameters were estimated using maximum likelihood estimation method. The usefulness of the Topp–Leone Lomax distribution was demonstrated using an airbone communication transceiver dataset and comparison were made with respect to the Topp–Leone Burr XII, Topp–Leone Flexible Weibull and Lomax distributions.


Generalized model Lomax distribution Mathematical statistics Topp–Leone family of distribution 



The authors are grateful to the anonymous reviewers for their useful comments and to Covenant University, Nigeria for providing an enabling environment for this research.


  1. 1.
    Abbas, S., Taqi, S. A., Mustapha, F., Murtaza, M., & Shahbaz, M. Q. (2017). Topp–Leone inverse Weibull distribution: Theory and application. European Journal of Pure and Applied Mathematics, 10(5), 1005–1022.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S., & Shahbaz, M. Q. (2016). Topp–Leone family of distributions: Some properties and application. Pakistan Journal of Statistics and Operation Research, 12(3), 443–451.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aryal, G. R., Ortega, E. M., Hamedani, G., & Yousof, H. M. (2016). The Topp–Leone generated Weibull distribution: Regression model, characterizations and applications. International Journal of Statistics and Probability, 6, 126.CrossRefGoogle Scholar
  4. 4.
    Bayoud, H. A. (2016). Estimating the shape parameter of Topp–Leone distribution based on progressive type II censored samples. REVSTAT-Statistical Journal, 14(4), 415–431.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Brito, E., Cordeiro, G. M., Yousof, H. M., Alizadeh, M., & Silva, G. O. (2017). The Topp–Leone odd log-logistic family of distributions. Journal of Statistical Computation and Simulation, 87(15), 3040–3058.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Feroze, N., & Aslam, M. (2013). N Bayesian Analysis of failure rate under Topp Leone distribution using complete and censored samples. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 7(3), 426–432.Google Scholar
  7. 7.
    Genc, A. (2012). Moments of order statistics of Topp–Leone distribution. Statistical Papers, 53(1), 117–131.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jorgensen, B. (1982). Statistical properties of the generalized inverse Gaussian distribution. New York: Springer.CrossRefzbMATHGoogle Scholar
  9. 9.
    Merovci, F., Khaleel, M. A., Ibrahim, N. A., & Shitan, M. (2016). The beta type X distribution: Properties with applications. SpringerPlus, 5, 697.CrossRefGoogle Scholar
  10. 10.
    MirMostafaee, S. M. T. K. (2014). On the moments of order statistics coming from the Topp–Leone distribution. Statistics and Probability Letters, 95, 85–91.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    MirMostafaee, S. M. T. K., Mahdizadeh, M., & Aminzadeh, M. (2016). Bayesian inference for the Topp–Leone distribution based on lower k-record values. Japan Journal of Industrial and Applied Mathematics, 33(3), 637–669.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Oguntunde, P. E., Adejumo, A. O., Okagbue, H. I., & Rastogi, M. K. (2016). Statistical properties and applications of a new Lindley exponential distribution. Gazi University Journal of Science, 29(4), 831–838.Google Scholar
  13. 13.
    Oguntunde P. E., Khaleel M. A., Ahmed M. T., Adejumo A. O., & Odetunmibi O. A. (2017). A new generalization of the Lomax distribution with increasing, decreasing and constant failure rate. Modelling and Simulation in Engineering, Article ID: 6043169, 6.Google Scholar
  14. 14.
    Owoloko, E. A., Oguntunde, P. E., & Adejumo, A. O. (2015). Performance rating of the transmuted exponential distribution: An analytical approach. SpringerPlus, 4, 818.CrossRefGoogle Scholar
  15. 15.
    Pourdarvish, A., Mirmostafaee, S. M. T. K., & Naderi, K. (2015). The exponentiated Topp–Leone distribution: Properties and application. Journal of Applied Environmental and Biological Sciences, 5(7S), 251–256.Google Scholar
  16. 16.
    Reyad, H. M., & Othman, S. A. (2017). The Topp–Leone Burr XII distribution: Properties and applications. British Journal of Mathematics and Computer Science, 21(5), 1–15.CrossRefGoogle Scholar
  17. 17.
    Sangsanit, Y., & Bodhisuwan, W. (2016). The Topp-Leone generator of distributions: properties and inferences. Songklanakarin Journal of Science and Technology, 38(5), 537–548.Google Scholar
  18. 18.
    Sultan, H., & Ahmad, S. P. (2016). Bayesian analysis of Topp–Leone distribution under different loss functions and different priors. Journal of Statistics Application and Probability Letters, 3(3), 109–118.CrossRefGoogle Scholar
  19. 19.
    Topp, C. W., & Leone, F. C. (1955). A family of J-shaped frequency functions. Journal of the American Statistical Association, 50(269), 209–219.MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Yousouf, H. M., Alizadeh, M., Jahanshahi, S. M. A., Ramires, T. G., Ghosh, I., & Hamedani, G. G. (2017). The transmuted Topp–Leone G family of distributions: Theory, characterizations and applications. Journal of Data Science, 15, 723–740.Google Scholar

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Authors and Affiliations

  1. 1.Department of MathematicsCovenant UniversityOtaNigeria
  2. 2.Department of Mathematics, Faculty of Computer Science and MathematicsUniversity of TikritTikritIraq

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