Article Sidebar

Download
PDF
Statistic
Read Counter : 610 Download : 643

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Main Article Content

Abstract




In this study, an alpha power inverted Kumaraswamy (APIK) distribution is introduced. The APIK distribution is de- rived by applying alpha power transformation to an inverted Kumaraswamy distribution. Some submodels and limiting cases of the APIK distribution are obtained as well. To the best of the authors’ knowledge, some of these distributions have not been introduced yet. Statistical inference of the APIK distribution, including survival and hazard rate func- tions, are obtained. Unknown parameters of the APIK distribution are estimated by using the maximum likelihood (ML), maximum product of spacings (MPS), and least squares (LS) methods. A Monte Carlo simulation study is con- ducted to compare the efficiencies of the ML estimators of the shape parameters α, β and λ of the APIK distribution with their MPS and LS counterparts. An application to a real data set is provided to show the implementation and modeling capability of the APIK distribution.




Keywords

Alpha power transformation Inverted Kumaraswamy distribution maximum likelihood maximum product of spacings least squares

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following License

CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.

 

How to Cite
Bagci, K., Erdogan, N., Arslan, T., & Celik, H. E. (2022). Alpha power inverted Kumaraswamy distribution: Definition, different estimation methods, and application. Pakistan Journal of Statistics and Operation Research, 18(1), 13-25. https://doi.org/10.18187/pjsor.v18i1.3327
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Abu-Moussa, M. H., & El-Din, M. M. M. (2018). On estimation and prediction for the inverted Kumaraswamy distribution based on general progressive censored samples. Pakistan Journal of Statistics and Operation Research, 14, 717-736, https://doi.org/10.18187/pjsor.v14i3.2103.
  2. Akgül, F. G., Şenoğlu, B., & Arslan, T. (2016). An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240, https://doi.org/10.1016/j.enconman.2016.02.026.
  3. Aldahlan, M. A. (2020). Alpha power transformed Log-Logistic distribution with application to breaking stress data. Advances in Mathematical Physics, Article ID 2193787, 1-9, https://doi.org/10.1155/2020/2193787.
  4. AL-Fattah, A. M., El-Helbawy, A. A., & Al-Dayian, G. R. (2017). Inverted Kumaraswamy distribution: Properties and estimation. Pakistan Journal of Statistics, 33, 37-61.
  5. 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 Operational Research, 17, 137-153, http://dx.doi.org/10.18187/pjsor.v17i1.3402.
  6. Aly, H. M., & Abuelamayem, O. A. (2020). Multivariate inverted Kumaraswamy distribution: Derivation and estimation. Mathematical Problems in Engineering, Article ID 6349523, 1-27, https://doi.org/10.1155/2020/6349523.
  7. Arslan, G., & Oncel, S. Y. (2017). Parameter estimation of some Kumaraswamy-G type distributions. Mathematical Sciences, 11, 131-138, https://doi.org/10.1007/s40096-017-0218-0.
  8. Arslan, T., Acitas, S., & ÅženoÄŸlu, B. (2017). Generalized Lindley and Power Lindley distributions for modeling the wind speed data. Energy Conversion and Management, 152, 300-311, https://doi.org/10.1016/j.enconman.2017.08.017.
  9. Bagci, K., Arslan, T., & Celik, H. E. (2021). Inverted Kumaraswamy distribution for modeling the wind speed data: Lake Van, Turkey. Renewable and Sustainable Energy Reviews, 135, 110110, https://doi.org/10.1016/j.rser.2020.110110.
  10. Bagci, K., Erdogan, N., Arslan, T., & Celik, H. E. (2019). Alpha power inverted Kumaraswamy distribution: Properties and application. International Conference on Computational Mathematics and Engineering Sciences (CMES-2019), 54. Antalya, Turkey.
  11. Barreto-Souza, W., & Simas, A. B. (2014). The exp-G family of probability distributions. Brazilian Journal of Probability and Statistics, 27, 84-109, https://www.jstor.org/stable/43601236.
  12. Basheer, A. M. (2019). Alpha power inverse Weibull distribution with reliability application. Journal of Taibah University for Science, 13, 423-432, https://doi.org/10.1080/16583655.2019.1588488.
  13. Biçer, H. D. (2019). Properties and inference for a new class of generalized Rayleigh distributions with an application. Open Mathematics, 17, 700-715, https://doi.org/10.1515/math-2019-0057.
  14. Bulut, Y. M., DoÄŸru, F. Z., & Arslan, O. (2021). Alpha power Lomax distribution: Properties and application. Journal of Reliability and Statistical Studies, 14, 17-32, https://doi.org/10.13052/jrss0974-8024.1412.
  15. Dey, S., Alzaatreh, A., Zhang, C., & Kumar, D. (2017). A new extension of generalized Exponential distribution with application to ozone data. Ozone: Science & Engineering, 39, 273-285, https://doi.org/10.1080/01919512.2017.1308817.
  16. Dey, S., Gosh, I., & Kumar, D. (2019). Alpha power transformed Lindley distribution: Properties and associated inference with application to earthquake data. Annals of Data Science, 6, 623-650, https://doi.org/10.1007/s40745-018-0163-2.
  17. Dey, S., Nassar, M., & 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, 385, 130-145, https://doi.org/10.1016/j.cam.2018.03.037.
  18. Erdogan, N., Bagci, K., Arslan, T., & Celik, H. E. (2021). Alpha power Maxwell distribution: Properties and application. Journal of Mathematical Modeling, 9, 585-598, https://doi.org/10.22124/JMM.2021.17987.1553.
  19. Hameed, B. A., Salman, A. N., & Kalaf, B. A. (2020). On the estimation of P(Y_1https://doi.org/10.24996/ijs.2020.61.4.18.
  20. Hassan, A. S., Elgarhy, M., Mohamd, R. E., & Alrajhi, S. (2019). On the alpha power transformed power Lindley distribution. Journal of Probability and Statistics, 8024769, 1-19, https://doi.org/10.1155/2019/8024769.
  21. Hassan, A. S., Mohamd, R. E., Elgarhy, M., & Fayomi, A. (2018). Alpha power transformed extended exponential distribution: properties and applications. Journal of Nonlinear Sciences and Applications, 12, 239-251, http://dx.doi.org/10.22436/jnsa.012.04.05.
  22. Ihtisham, S., Khalil, A., Manzoor, S., Khan, S. A., & Ali, A. (2019). Alpha-power Pareto distribution:Its properties and applications. PLoS ONE, 14, 1-15, https://doi.org/10.1371/journal.pone.0218027.
  23. Iqbal, Z., Tahir, M. M., Riaz, N., Ali, S. A., & Ahmad, M. (2017). Generalized inverted Kumaraswamy distribution: Properties and application. Open Journal of Statistics, 7, 645-662, https://doi.org/10.4236/ojs.2017.74045.
  24. Jamal, F., Nasir, M. A., Ozel, G., Elgarhy, M., & Khan, N. M. (2019). Generalized inverted Kumaraswamy generated family of distributions: Theory and applications. Journal of Applied Statistics, 46, 356-365, https://doi.org/10.1080/02664763.2019.1623867.
  25. Jones, M. C. (2009). Kumaraswamy's distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 6, 70-81, https://doi.org/10.1016/j.stamet.2008.04.001.
  26. Jones, M. C. (2018). Letter to the Editor concerning ``A new method for generating distributions with an application to exponential distribution'' and ``Alpha power Weibull distribution: Properties and applications''. Communications in Statistics-Theory and Methods, 47, 5096, https://doi.org/10.1080/03610926.2017.1386314.
  27. Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46, 79-88, https://doi.org/10.1016/0022-1694(80)90036-0.
  28. Lee, C., Famoye, F., & Alzaatreh, A. Y. (2013). Methods for generating families of univariate continuous distributions in the recent decades. Wiley Interdisciplinary Reviews: Computational Statistics, 5, 219-238, https://doi.org/10.1002/wics.1255.
  29. Mahdavi, A., & Kundu, D. (2017). A new method for generating distributions with an application to Exponential distribution. Communications in Statistics-Theory and Methods, 46, 6543-6557, https://doi.org/10.1080/03610926.2015.1130839.
  30. Mead, M. E., Cordeiro, G. M., Afify, A. Z., & Al-Mofleh, H. (2019). The alpha power transformation family: Properties and applications. Pakistan Journal of Statistics and Operational Research, 15, 525-545, https://doi.org/10.18187/pjsor.v15i3.2969.
  31. Nadarajah, S., Nassiri, V., & Mohammadpour, A. (2014). Truncated-exponential skew-symmetric distributions. Statistics, 48, 872-895, https://doi.org/10.1080/02331888.2013.821474.
  32. Nassar, M., Afify, A. Z., & Shakhatreh, M. K. (2020). Estimation methods of alpha power Exponential distribution with applications to engineering and medical data. Pakistan Journal of Statistics and Operational Research, 16, 149-166, https://doi.org/10.18187/pjsor.v16i1.3129.
  33. Nassar, M., Alzaatreh, A., Mead, M., & Abo-Kasem, O. (2017). Alpha power Weibull distribution: Properties and applications. Communications in Statistics-Theory and Methods, 46, 10236-10252, https://doi.org/10.1080/03610926.2016.1231816.
  34. Nichols, M. D., & Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International, 22, 141-151, https://doi.org/10.1002/qre.691.
  35. Ramadan, D. A., & Magdy, A. (2018). On the alpha-power inverse Weibull distribution. International Journal of Computer Applications, 11, 6-12, https://doi.org/10.5120/ijca2018917657.
  36. Reyad, H., Jamal, F., Othman, S., & Yahia, N. (2019). The Topp-Leone generalized inverted Kumaraswamy distribution: Properties and applications. Asian Research Journal of Mathematics, 13, 1-15, https://doi.org/10.9734/arjom/2019/v13i330107.
  37. Sherwani, R. E. K., Waqas, M., Saeed, N., Farooq, M., Raza, M. A., & Jamal, F. (2021). Transmuted inverted Kumaraswamy distribution: Theory and applications. Punjab University Journal of Mathematics, 53, 29-45.
  38. Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Jhonson's translation system. Journal of Statistical Computation and Simulation, 24, 271-297, https://doi.org/10.1080/00949658808811068.
  39. Unal, C., Cakmakyapan, S., & Ozel, G. (2018). Alpha power inverted Exponential distribution: Properties and application. Gazi Journal of Science, 31, 957-965.
  40. Usman, R. M., & ul Haq, M. A. (2020). The Marshall-Olkin extended inverted Kumaraswamy distribution: Theory and applications. Journal of King Saud University, 32, 356-365, https://doi.org/10.1016/j.jksus.2018.05.021.
  41. Volovskiy, G., & Kamps, U. (2020). Maximum product of spacings prediction of future record values. Metrika, 83, 853-868, https://doi.org/10.1007/s00184-020-00767-1.