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In this article we have discussed linear mixing of two exponentiated distribution. The proposed model is named as exponentiated exponential-exponentiated Weibull (EE-EW) distribution. The proposed distribution generalize several existing distributions. We study several characteristics of the proposed distribution including moment, moment generating function, reliability and hazard rate functions. An empirical study is presented for mean, variance, coefficient of skewness, and coefficient of kurtosis. The method of maximum likelihood is used for the estimation of parameters. For the illustration purpose, we have use two real-life data set for application. The results justify the capability of the new model.


Exponentiated Exponential Exponentiated Weibull Emprical Study Inference Maximum likelihood

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How to Cite
Abbas, S., Mohsin, M., Shahbaz, S. H., & Qaiser Shahbaz, M. (2020). Exponentiated Exponential-Exponentiated Weibull Linear Mixed Distribution: Properties and Applications. Pakistan Journal of Statistics and Operation Research, 16(3), 517-527.


  1. Abbas, S., Ozal, G., Shahbaz, S. H., and Shahbaz, M. Q. (2019). A new generalized weighted weibull distribution. Pakistan Journal of Statistics and Operation Research, 15(1):161–178.
  2. Abdi, A. and Kaveh, M. (1998). K distribution: An appropriate substitute for rayleigh-lognormal distribution in fading-shadowing wireless channels. Electronics Letters, 34(9):851–852.
  3. Abu-Zinadah, H. H. (2010). A study on mixture of exponentiated pareto and exponential distributions. Journal of Applied Sciences Research, 6(4):358–376.
  4. Al-Hussaini, E. (1999). Bayesian prediction under a mixture of two exponential components model based on type i censoring. Journal of Applied Statistical Science, 8:173–185.
  5. Al-Hussaini, E. K., Al-Dayian, G. R., and Adham, S. A. (2000). On finite mixture of two-component gompertz lifetime model. Journal of Statistical Computation and Simulation, 67(1):20–67.
  6. Al-Zahrani, B. and Sagor, H. (2014). The poisson-lomax distribution. Revista Colombiana de Estadıstica, 37(1):225–245.
  7. Badr, M. and Shawky, A. (2014). Mixture of exponentiated frechet distribution. Life Science Journal, 11(3):392–404.
  8. Bakoban, R. (2010). A study on mixture of exponential and exponentiated gamma distributions. Advances and Applications in Statistical Sciences, 2(1):101–127.
  9. Bartoszewicz, J. (2002). Mixtures of exponential distributions and stochastic orders. Statistics & probability letters, 57(1):23–31.
  10. Bethea, R. M. (1995). Statistical methods for engineers and scientists, volume 144. CRC Press.
  11. Birnbaum, Z. W. and Saunders, S. C. (1969). Estimation for a family of life distributions with applications to fatigue. Journal of Applied probability, pages 328–347. DOI:
  12. Gharib, M. (1995). Two characterizations of a gamma mixture distribution. Bulletin of the Australian Mathematical Society, 52(3):353–358.
  13. Gharib, M. (1996). Characterizations of the exponential distribution via mixing distributions. Microelectronics Reliability, 36(3):293–305.
  14. Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43(1):117–130.
  15. Hanook, S., Shahbaz, M. Q., Mohsin, M., and Golam Kibria, B. (2013). A note on beta inverse-weibull distribution. Communications in Statistics-Theory and Methods, 42(2):320–335.
  16. Jaheen, Z. F. (2005). On record statistics from a mixture of two exponential distributions. Journal of Statistical Computation and Simulation, 75(1):1–11.
  17. Jewell, N. P. (1982). Mixtures of exponential distributions. The annals of statistics, pages 479–484. DOI:
  18. Lindsay, B. G. (1995). Mixture models: theory, geometry and applications. In NSF-CBMS regional conference series in probability and statistics, pages i–163. JSTOR.
  19. Mubarak, M. (2011). Mixture of two Frechet distributions: Properties and estimation. International Journal of Engineering Science and Technology (IJEST), 3(5):4067–4073.
  20. Mudholkar, G. S. and Srivastava, D. K. (1993). Exponentiated weibull family for analyzing bathtub failurerate data. IEEE transactions on reliability, 42(2):299–302.
  21. Nair, M. T. and Abdul, S. E. (2010). Finite mixture of exponential model and its applications to renewal and reliability theory. Journal of Statistical Theory and Practice, 4(3):367–373.
  22. Nassar, M. (1988). Two properties of mixtures of exponential distributions. IEEE transactions on reliability, 37(4):383–385.
  23. Nassar, M. and Mahmoud, M. (1985). On characterizations of a mixture of exponential distributions. IEEE transactions on reliability, 34(5):484–488.
  24. Prudnikov, A., Brychkov, Y. A., and Marichev, O. I. (1986). Integrals and series (volumes 1, 2 and 3).
  25. Radhakrishna, C., Dattatreya Rao, A., and Anjaneyulu, G. (1992). Estimation of parameters in a two component mixture generalized gamma distribution. Communications in statistics-theory and methods, 21(6):1799–1805.
  26. Rider, P. R. (1961). The method of moments applied to a mixture of two exponential distributions. The Annals of Mathematical Statistics, 32(1):143–147.
  27. Rodriguez, R. N. (1977). A guide to the burr type xii distributions. Biometrika, 64(1):129–134.
  28. Shawky, A. and Bakoban, R. (2009). On finite mixture of two-component exponentiated gamma distribution. Journal of Applied Sciences Research, 5(10):1351–1369.
  29. Soliman, A. A. (2006). Estimators for the finite mixture of Rayleigh model based on progressively censored data. Communications in Statistics Theory and Methods, 35(5):803–820.
  30. Sultan, K. S., Ismail, M. A., and Al-Moisheer, A. S. (2007). Mixture of two inverse weibull distributions: Properties and estimation. Computational Statistics & Data Analysis, 51(11):5377–5387.
  31. Titterington, D. M., Smith, A. F., and Makov, U. E. (1985). Statistical analysis of finite mixture distributions. Wiley,.

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