Main Article Content

Abstract

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

Keywords

Marshall-Olkin Alpha Power Rayleigh distribution Maximum likelihood estimation Bootstrap estimation

Article Details

How to Cite
Almetwally, E. M., Afify, A. Z., & Hamedani, G. G. (2021). Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications. Pakistan Journal of Statistics and Operation Research, 17(3), 745-760. https://doi.org/10.18187/pjsor.v17i3.3473

References

  1. Afify, A. Z., Cordeiro, G. M., Yousof, H. M., Saboor, A. and Ortega, E. M. (2018). The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate. Hacettepe Journal of Mathematics and Statistics, 47, 365-381.
  2. Aldahlan, M. and Afify, A. Z. (2018). The odd exponentiated half-logistic Burr XII distribution. Pakistan Journal of Statistics and Operation Research, 14, 305-317. DOI: https://doi.org/10.18187/pjsor.v14i2.2285
  3. Ahmad, H. H. and Almetwally, E. (2020). Marshall-Olkin generalized Pareto distribution: Bayesian and non Bayesian estimation. Pakistan Journal of Statistics and Operation Research, 16, 21-33. DOI: https://doi.org/10.18187/pjsor.v16i1.2935
  4. Almetwally, E. M., Sabry, M. A., Alharbi, R., Alnagar, D., Mubarak, S. A., Hafez, E. H. (2021). Mar- shall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring. Complexity, 2021. https://doi.org/10.1155/2021/5533799 DOI: https://doi.org/10.1155/2021/5533799
  5. Almetwally, E. M. Marshall Olkin Alpha Power Extended Weibull Distribution: Different Methods of Estimation based on Type I and Type II Censoring. Gazi University Journal of Science, 1-23. https://doi.org/10.35378/gujs.741755. DOI: https://doi.org/10.35378/gujs.741755
  6. Almongy, H. M., Almetwally, E. M., Mubarak, A. E. (2021). Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics. Pakistan Journal of Statistics and Operation Research, 17(1), 137-153. DOI: https://doi.org/10.18187/pjsor.v17i1.3402
  7. Basheer, A. M. (2019). Alpha power inverse Weibull distribution with reliability application. Journal of Taibah University for Science, 13, 423-432. DOI: https://doi.org/10.1080/16583655.2019.1588488
  8. Dey, S., Ghosh, I. and Kumar, D. (2018). Alpha-power transformed lindley distribution: properties and asso- ciated inference with application to earthquake data. Annals of Data Science, 1-28. DOI: https://doi.org/10.1007/s40745-018-0163-2
  9. Dey, S., Nassar, M. and Kumar, D. (2019). Alpha power transformed inverse Lindley distribution: a distribu- tion with an upside-down bathtub-shaped hazard function. Journal of Computational and Applied Mathe- matics, 348, 130-145. DOI: https://doi.org/10.1016/j.cam.2018.03.037
  10. Elbatal, I., Ahmad, Z., Elgarhy, B. M. and Almarashi, A. M. (2018). A new alpha power transformed family of distributions: properties and applications to the Weibull model. Journal of Nonlinear Science and Applications, 12, 1-20. DOI: https://doi.org/10.22436/jnsa.012.01.01
  11. Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan, L. (2007). Marshall-Olkin extended Lomax distribution and
  12. its application to censored data. Commun. Stat. Theory Methods, 36, 1855-1866.
  13. Ghitany, M. E., Al-Hussaini, E. K. and Al-Jarallah, R. A. (2005). Marshall-Olkin extended Weibull distribution and its application to censored data. Journal of Applied Statistics, 32, 1025-1034. DOI: https://doi.org/10.1080/02664760500165008
  14. Glanzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, 75-84. DOI: https://doi.org/10.1007/978-94-009-3965-3_8
  15. Glanzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics: A Journal of Theoretical and Applied Statistics, 21, 613-618. DOI: https://doi.org/10.1080/02331889008802273
  16. Hassan, A. S. and Abd-Allah, M. (2019). On the inverse power Lomax distribution. Annals of Data Science, DOI: https://doi.org/10.1007/s40745-018-0183-y
  17. , 259-278.
  18. Karian, Z. A. and Dudewicz, E. J. (1998). Modern statistical, systems, and GPSS simulation. CRC press.
  19. 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. DOI: https://doi.org/10.1080/03610926.2015.1130839
  20. Malik, A. S. and Ahmad, S.P. (2017). Alpha power Rayleigh distribution and its application to life time data.
  21. International Journal of Enhanced Research in Management, Computer Applications, 6, 212-219.
  22. Mansoor, M., Tahir, M. H., Alzaatreh, A., Cordeiro, G. M., Zubair, M. and Ghazali, S. S. (2016). An extended
  23. Frechet distribution: properties and applications. Journal of Data Science, 14, 167-188. ´ DOI: https://doi.org/10.6339/JDS.201601_14(1).0010
  24. Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with
  25. application to the exponential and Weibull families. Biometrika, 84, 641-652.
  26. Mead, M. E., Cordeiro, G. M., Afify, A. Z. and Al Mofleh, H. (2019). The alpha power transformation family:
  27. properties and applications. Pakistan Journal of Statistics and Operation Research, 15, 525-545.
  28. MirMostafaee, S. M. T. K., Mahdizadeh, M. and Lemonte, A. J. (2017). The Marshall-Olkin extended generalized Rayleigh distribution: properties and applications. Commun. Stat. Theory Methods, 46, 653-671. DOI: https://doi.org/10.1080/03610926.2014.1002937
  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. DOI: https://doi.org/10.1080/03610926.2016.1231816
  30. Nassar, M., Kumar, D., Dey, S., Cordeiro, G. M. and Afify, A. Z. (2019). The Marshall-Olkin alpha power
  31. family of distributions with applications. Journal of Computational and Applied Mathematics, 351, 41-53.
  32. Okasha, H. M. and Kayid, M. (2016). A new family of Marshall-Olkin extended generalized linear exponential distribution. Journal of Computational and Applied Mathematics, 296, 576-592. DOI: https://doi.org/10.1016/j.cam.2015.10.017