The Exponentiated Gumbel Lomax Distribution: Properties and Applications


  • Uchenna Ugwunnaya Uwadi Alex Ekwueme Federal University Ndufu-alike, Nigeria
  • Elebe Emmanuel Nwezza Alex Ekwueme Federal University Ndufu-alike, Nigeria
  • Chukwuemeka Onwuzuruike Omekara Micheal Okpara University of Agriculture, Umudike, Nigeria



Exponentiated Gumbel distribution, Lomax distribution, Moments, Maximum likelihood estimation


A new five-parameter distribution called exponentiated Gumbel Lomax (EGuL) is proposed and studied. The proposed distribution has reverse J-shaped, inverted bathtub-shaped and J-shaped hazard rate function making it suitable for modeling survival and lifetime data. The density of the new distribution is expressed as a linear combination of the exponentiated density of the Lomax distribution. We derive the explicit expression for the quantile function, moments, incomplete moment, moment of residual life, entropy and order statistics of EGuL distribution. The estimation of the parameters of the new model is done using the method of maximum likelihood. A simulation study is employed to ascertain the performance of the maximum likelihood estimates. Two applications are used to illustrate that the new distribution provides a better fit compared to other distributions with the same baseline.


M. V. AARSET (1987). How to identify bathtub hazard rate. IEEE Transactions Reliability, 36, no. 1, pp. 106–108.

R. AL-AQTASH, F. FAMOYE, C. LEE (2015). On generating a new family of distributions using the logit function. Journal of Probability and Statistical Science, 13, no. 1, pp. 135–152.

A. ALGHAMDI (2018). Study of Generalized Lomax Distribution and Change Point Problem. A Dissertation, Bowling Green State University.

M. ALIZADEH, G. M. CORDEIRO, E. DE BRITO, C. B. DEMETRIO (2015). The beta Marshall-Olkin family of distributions. Journal of Statistical distributions and Applications, 2, no. 4, pp. 2–18.

M. ALMHEIDAT, F. FAMOYE, C. LEE (2015). Some generalized families of Weibull distribution: properties and applications. International Journal of Statistics and Probability, 4, no. 3, pp. 18–35.

S. K.ASHOUR, M.A. ELTEHIWY (2013). Transmuted exponentiated Lomax distribution. Australian Journal of Basic and Applied Sciences, 7, no. 7, p. 658–667.

T. BJERKEDAL (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Epidemilology, 72, no. 1, pp. 130–148.

G. M. CORDERIO, A. Z. AFIFY, H. YOUSOF, S. CAKMAKYAPAN, G. OZEL (2018). The Lindley Weibull distribution: properties and applications. Anais da Academia Brasileira de Ciencias, 90, no. 3, pp. 2579–2598.

S. DEY, M. NASSAR, D. KUMAR, A. ALZAATREH, M. H. TAHIR (2019). A new lifetime distribution with decreasing and upside-down bathtub-shaped hazard rate function. STATISTICA, 79, no. 4, pp. 399–426.

M. ELGARHY, M. SHAKIL, B. M. KIBRIA (2017). Exponentiated Weibull-exponential distribution with applications. Applications and Applied Mathematics: An International journal, 12, pp. 710–725.

F. GALTON (1983). Enquires into human faculty and its development. Macmillan and company, London.

M. E. GHITANY, F. A. AL-AWADHI, L. A. ALKHALFAN (2007). Marshall–Olkin extended Lomax distribution and its application to censored data. Communications in Statistics-Theory and Methods, 36, p. 1855–1866.

A. S. HASSAN, M. ABD-ALLAH (2018). Exponentiated Weibull-Lomax distribution: properties and estimation. Journal of Data Science, 16, no. 2, pp. 277–298.

C. LEE, F. FAMOYE, A. ALZAATREH (2013). Methods for generating families of univariate continuous distributions in the recent decades. WIREs Comput Stat. URL

A. J. LEMONTE, G. M. CORDEIRO (2013). An extended Lomax distribution. Statistics, 47, no. 4, pp. 800–816.

K. S. LOMAX (1954). Business failures: another example of the analysis of failure data. Journal of the American Statistical Association, 49, no. 268, p. 847–852.

J. J. MOOR (1988). A quantile alternative for kurtosis. The Statistician, 37, no. 1, pp. 25–32.

G. S. MUDHOLKAR, D. K. SRIVASTAVA, G. D. KOLLIA (1996). A generalization of the Weibull distribution with application to the analysis of survival data. Journal of the American Statistical Association, 91, no. 436, pp. 1575–1583.

E. E. NWEZZA, F. I. UGWUOWO (2020). The Marshall-Olkin Gumbel-Lomax distribution; properties and applications. Heliyon, 6, no. 3, pp. 1–13.

A. PATHAK, A. CHATURVEDI (2013). Estimation of the reliability function for fourparameter exponentiated generalized Lomax distribution. International Journal of Scientific Engineering Research, 5, no. 1, pp. 1171–1180.

E. A. RADY,W. A. HASSANEIN, T. A. ELHADDAD (2016). The power Lomax distribution with an application to bladder cancer data. Springer Plus, 5, p. 1838.

A. RENYI (1961). On measures of entropy and information. In Proceedings of the fourth Beckley Symposium on Mathematical Statistics and Probability, Holt, Rinehart and Winstons, pp. 547–561.

H. M. SALEM (2014). The exponentiated Lomax distribution: different estimation methods. American Journal of Applied Mathematics and Statistics, 2, no. 6, pp. 364–368.

M. H. TAHIR, G. M. CORDEIRO, M. MANSOOR, M. ZUBAIR (2015). The Weibull-Lomax distribution: properties and applications. Hacettepe Journal of Mathematics and Statistics, 45, no. 2, pp. 245–265.

M. H. TAHIR, M.A.HUSSAIN, G. M.CORDEIRO, G. G.HAMEDANI, M.MANSOOR, M. ZUBAIR (2016). The Gumbel-Lomax distribution: properties and applications. Journal of Statistical Theory and Applications, 15, no. 1, pp. 61–79.

U.U.UWADI, E.W.OKEREKE, C. O.OMEKARA (2019). Exponentiated Gumbel family of distributions: properties and applications. International Journal of Basic Science and Technology, 5, no. 2, pp. 100–117.




How to Cite

Uwadi, U. U., Nwezza, E. E., & Omekara, C. O. (2024). The Exponentiated Gumbel Lomax Distribution: Properties and Applications. Statistica, 82(4), 433–459.