The Weibull-Power Lomax Distribution: Properties and Application


  • Nafiu Abubakar Hussain Ahmadu Bello University, Samaru Zaria, Kaduna State,Nigeria
  • S.I.S. Doguwa Department of Statistics
  • Abubakar Yahaya Ahmadu Bello University, Samaru Zaria, Kaduna State,Nigeria


Weibull-G, Power-Lomax Distribution, Hazard function, Likelihood estimation


Authors: Hussain Nafi’u Abubakar, Doguwa S.I.S., and Yahaya Abubakar

Received 5 May 2020/Accepted 1 December 2020/

The power lomax distribution is a very good model in modelling real life financial and reliability data. However, we extend the power lomax distribution with the Weibull G family in order to increase its flexibility and usage. Therefore, in this paper a new five-parameter distribution is introduced called the Weibull-Power Lomax distribution. The structural properties of the proposed distribution such as hazard function, moments, probability weighted moments, distribution of order statistics and quantile function are derived. The maximum likelihood estimation technique is employed to estimate the parameters of the proposed distribution. To also prove the increased flexibility and performance of the distribution, it is used to model 63 observations of strengths of 1.5cm glass fibers, along with its other competing distributions. The results indicate that the proposed distribution fit the glass fiber data and performs much better than its competitors.


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Author Biographies

Nafiu Abubakar Hussain, Ahmadu Bello University, Samaru Zaria, Kaduna State,Nigeria

Department of Statistics

S.I.S. Doguwa, Department of Statistics

Ahmadu Bello University, Samaru Zaria, Kaduna State,Nigeria

Abubakar Yahaya, Ahmadu Bello University, Samaru Zaria, Kaduna State,Nigeria

Department of Statistics


Abdul-Moniem, I. B. (2017). Order statistics from power lomax distribution. International Journal

of Innovative Science, Engineering and Technology, 4:1–4.

Atkinson, A. and Harrison, A. (1978). Distribution of personal wealth in britain cambridge university


Bourguignon, M., Silva, R. B., and Cordeiro, G. M. (2014). The weibull-g family of probability

distributions. Journal of Data Science, 12(1):53–68.

Bryson, M. C. (1974). Heavy-tailed distributions: properties and tests. Technometrics, 16(1):61–68.

Harris, C. M. (1968). The pareto distribution as a queue service discipline. Operations Research,


Hassan, A. S. and Al-Ghamdi, A. S. (2009). Optimum step stress accelerated life testing for lomax

distribution. Journal of Applied Sciences Research, 5(12):2153–2164.

Holland, O., Golaup, A., and Aghvami, A. (2006). Traffic characteristics of aggregated module

downloads for mobile terminal reconfiguration. IEE Proceedings-Communications, 153(5):683–

Lomax, K. (1954). Business failures: Another example of the analysis of failure data. Journal of the

American Statistical Association, 49(268):847–852.

Rady, E.-H. A., Hassanein, W., and Elhaddad, T. (2016). The power lomax distribution with an

application to bladder cancer data. SpringerPlus, 5(1):1838.

Smith, R. L. and Naylor, J. (1987). A comparison of maximum likelihood and bayesian estimators

for the three-parameter weibull distribution. Journal of the Royal Statistical Society: Series C

(Applied Statistics), 36(3):358–369.

Tahir, M. H., Cordeiro, G. M., Alizadeh, M., Mansoor, M., Zubair, M., and Hamedani, G. G. (2015a).

The odd generalized exponential family of distributions with applications. Journal of Statistical

Distributions and Applications, 2(1):1.

Tahir, M. H., Cordeiro, G. M., Mansoor, M., and Zubair, M. (2015b). The weibull-lomax distribution:

properties and applications. Hacettepe Journal of Mathematics and Statistics, 44(2):461–480