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This paper addresses the estimation of the unknown parameters of the alpha
power exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameter
estimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real data
sets from the elds of engineering and medicine. Finally, we use the maximum
likelihood method to derive the estimates of the distribution parameters under
competing risks data and analyze one real data set.


Alpha power transformation hazard rate function maximum likelihood estimation method of maximum product spacing simulation

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How to Cite
Nassar, M., Afify, A. Z., & Shakhatreh, M. (2020). Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data. Pakistan Journal of Statistics and Operation Research, 16(1), 149-166.


  1. Afify, A. Z. and Mohamed, O. A. (2020). A new three-parameter exponential distribution with variable shapes for the hazard rate: estimation and applications. Mathematics, 8, 1-17.
  2. Afify, A. Z., Nassar, M., Cordeiro, G. M. and Kumar, D. (2020). The Weibull Marshall–Olkin Lindley distribution: properties and estimation. Journal of Taibah University for Science, 14, 192-204.
  3. Afify, A. Z., Suzuki, A. K., Zhang, C. and Nassar, M. (2019). On three-parameter exponential distribution: properties, Bayesian and non-Bayesian estimation based on complete and censored samples. Commun. Stat.Simul. Comput. Doi:10.1080/03610918.2019.1636995.
  4. Ashour, S. K. and Nassar, M. (2014). Analysis of exponential distribution under adaptive type-I progressive hybrid censored competing risks data. Pak. J. Stat. Oper. Res., 10, 2014.
  5. Ashour, S. K and Nassar, M. (2017). Inference for Weibull distribution under adaptive type-I progressive hybrid censored competing risks data. Commun. Stat. Theory Methods, 46, 4756-4773.
  6. Cheng, R. C. H., and Amin, N. A. K. (1979). Maximum product of spacings estimation with applications to the lognormal distribution. Technical report, Department of Mathematics, University of Wales.
  7. Cheng, R. C. H., and Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. J. R. Statist. Soc. B, 45, 394–403.
  8. Cordeiro, G. M., Afify, A. Z., Yousof, H. M., Cakmakyapan, S. and Ozel, G. (2018). The Lindley Weibull distribution: properties and applications. Anais da Academia Brasileira de Ci´Incias, 90, 2579-2598.
  9. Cramer, E. and Schmiedt, A. B. (2011). Progressively type-II censored competing risks data from Lomax distribution. Computational Statistics and Data Analysis, 55, 1285-1303.
  10. D’Agostino, R. B. (1986). Goodness-of-fit-techniques. Statistics: A Series of Textbooks and Monographs. Taylor & Francis.
  11. Dey, A., Alzaatreh, A., Zhang, C. and Kumar, D. (2017). A new extension of generalized exponential distribution with application to ozone data. Ozone: Science & Engineering, 39, 273-285.
  12. Dey, S., Ghosh, I. and Kumar, D. (2019). Alpha-power transformed Lindley distribution: properties and associated inference with application to earthquake data. Annals of Data Science.
  13. Dey, S., Nassar, M. and Kumar, D. (2019). Alpha power transformed inverse Lindley distribution: a distribution with an upside-down bathtub-shaped hazard function. Journal of Computational and Applied Mathematics, 348, 130-145.
  14. Gupta, R. D. and Kundu, D. (2001). Generalized exponential distribution: different method of estimations. Journal of Statistical Computation and Simulation, 69, 315-337.
  15. Hoel, D. G. (1972). A representation of mortality data by competing risks. Biometrics, 28, 475-488.
  16. Hosking, J. R. M. (1990). L-Moments: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. Series B, 52, 105–124.
  17. Jones, M. C. (2004). Families of distributions arising from distributions of order statistics. Test, 13, 1-43.
  18. Khan, M. S., King, R. and Hudson, I. (2017). Transmuted generalized exponential distribution: a generalization of the exponential distribution with applications to survival data. Commun. Stat. Simul.Comput., 46, 4377-4398.
  19. Kundu, D., Kannan, N. and Balakrishnan, N. (2004). Analysis of progressivelycensored competing risks data. Handbook of Statistics, vol. 23, eds.,Balakrishnan, N. and Rao, C.R., Elsevier, New York.
  20. Mahdavi, A. and D. Kundu. (2017). A new method for generating distributions with an application to exponential distribution. Commun. Stat. Theory Methods, 46, 6543-6557.
  21. Mansoor, M., Tahir, M. H., Cordeiro, G. M., Provost, S. B. and Alzaatreh, A. (2018). The Marshall-Olkin logistic-exponential distribution. Commun. Stat. Theory Methods. Doi: 10.1080/03610926.2017.1414254.
  22. Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, 641-652.
  23. Mead, M. E., Cordeiro, G. M., Afify, A. Z. and Al Mofleh, H. (2019). The alpha power transformation family: properties and applications. Pak. J. Stat. Oper. Res., 15, 525-545.
  24. Murthy, D. P., Xie, M. and Jiang, R. (2004). Weibull models. John Wiley & Sons.
  25. Nadarajah, S. and Kotz, S. (2006). The beta exponential distribution. Reliability engineering & system safety, 91, 689-697.
  26. Nadarajah, S. and Okorie, I. E. (2018). On the moments of the alpha power transformed generalized exponential distribution. Ozone: Science & Engineering, 40, 330-335.
  27. Nassar, M., Afify, A. Z., Dey, S. and Kumar, D. (2018a). A new extension of weibull distribution: properties and different methods of estimation. Journal of Computational and Applied Mathematics, 336, 439-457.
  28. Nassar, M., Alzaatreh, A., Abo-Kasem, O., Mead, M. and Mansoor, M. (2018b). A new family of generalized distributions based on alpha power transformation with application to cancer data. Annals of Data Science, 5, 421-436.
  29. Nassar, M. Alzaatreh, A., Mead, M. and Abo-Kasem, O. (2017). Alpha power Weibull distribution: properties and applications. Commun. Stat. Theory Methods. 46, 10236-10252.
  30. Nassar, M., Dey, S. and Kumar, D. (2018c). A new generalization of the exponentiated Pareto distribution with an application. Amer. J. Math. Manag. Sci., 37, 217-242.
  31. Nassar, M., Kumar, D., Dey, S., Cordeiro, G. M. and Afify, A. Z. (2019). The Marshall–Olkin alpha power family of distributions with applications. Journal of Computational and Applied Mathematics, 351, 41-53.
  32. Sen, S., Afify, A. Z., Al-Mofleh, H. and Ahsanullah, M. (2019). The quasi xgamma-geometric distribution with application in medicine. Filomat, 33, 5291-5330.
  33. Shakhatreh, M. K., Lemonte, A. J. and Cordeiro, G. M. (2019). On the generalized extended exponential-Weibull distribution: properties and different methods of estimation. International Journal of Computer Mathematics. DOI:10.1080/00207160.2019.1605062.
  34. Weibull, W. (1951). A statistical distribution function of wide applicability. ASME Trans. J. Appl. Mech., 18, 293-297.