Main Article Content
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.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan, L. (2007). Marshall-Olkin extended Lomax distribution and
- its application to censored data. Commun. Stat. Theory Methods, 36, 1855-1866.
- 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
- 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
- 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
- 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
- , 259-278.
- Karian, Z. A. and Dudewicz, E. J. (1998). Modern statistical, systems, and GPSS simulation. CRC press.
- 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
- Malik, A. S. and Ahmad, S.P. (2017). Alpha power Rayleigh distribution and its application to life time data.
- International Journal of Enhanced Research in Management, Computer Applications, 6, 212-219.
- Mansoor, M., Tahir, M. H., Alzaatreh, A., Cordeiro, G. M., Zubair, M. and Ghazali, S. S. (2016). An extended
- Frechet distribution: properties and applications. Journal of Data Science, 14, 167-188. ´ DOI: https://doi.org/10.6339/JDS.201601_14(1).0010
- 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.
- Mead, M. E., Cordeiro, G. M., Aﬁfy, A. Z. and Al Moﬂeh, H. (2019). The alpha power transformation family:
- properties and applications. Pakistan Journal of Statistics and Operation Research, 15, 525-545.
- 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
- 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
- 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.
- 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