A new generalization of the Remkan distribution and its application to survival data

Main Article Content

O. R. Uwaeme
Glory Chinonye Nwagwu
Chinedu Kingsley Obasi
https://orcid.org/0009-0007-2862-5159
Ligeiaziba Sylva
https://orcid.org/0000-0001-6703-764X

Abstract

Due to the increasing need for flexibility in baseline distribution, this study proposes a new generalization of the two-parameter Remkan distribution using the Alpha Power Transformed technique. Important statistical properties of the new distribution such as the reliability measures, the order statistics, moments and other related measures, and moment generating function were derived and the model parameters estimated using the maximum likelihood estimate technique. Finally, the flexibility of the new distribution was illustrated using two real life datasets and the results showed that the new Alpha Power Transformed Remkan distribution was the best amongst other competing three-parameter distributions.

Article Details

How to Cite
Uwaeme, O. . R., Nwagwu, G. C., Obasi, C. K., & Sylva , L. (2026). A new generalization of the Remkan distribution and its application to survival data. Brazilian Journal of Biometrics, 44(3), e-44868. https://doi.org/10.28951/bjb.v44i3.868
Section
Articles

References

1. Abdi, M., Asgharzadeh, A., Bakouch, H. S. & Alipour, Z. A New Compound Gamma and Lindley Distribution with Application to Failure Data. Austrian Journal of Statistics 48, 54–75 (2019). https://doi.org/10.17713/ajs.v48i3.843

2. Aderoju, S. Samade Probability Distribution: Its Properties and Application to Real Lifetime Data. Asian Journal of Probability and Statistics 14, 1–11 (2021). https://doi.org/10.9734/ajpas/2021/v14i130317

3. Aijaz, A., Jallal, M., Ain, S. Q. U. & Tripathi, R. The Hamza Distribution with Statistical Properties and Applications. Asian Journal of Probability and Statistics 8, 28–42 (2020). https://doi.org/10.9734/AJPAS/2020/v8i130196

4. Akpan, N. P. A New Generalization of the Copoun Distribution: Identifiability and Properties. Journal of Research in Applied Mathematics 10, 30–38 (2024).

5. Akpan, N. P. The Inverse Remkan Distribution and its Applications to Uncensored Data. Journal of Research in Applied Mathematics 10, 43–53 (2024).

6. Akpan, N. P. & Uwaeme, O. R. On the Statistical Properties of the Remkan Distribution. Earthline Journal of Mathematical Sciences 14, 333–347 (2024). https://doi.org/10.34198/ejms.14224.

7. Alzaatreh, A., Lee, C. & Famoye, F. A new method for generating families of continuous distributions. Metron 71, 63–79 (2013).

8. Azzalini, A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 171–178 (1985).

9. Barlow, R. & Proschan, F. Statistical Theory of Reliability and Life-Testing: Probability Models Reprint. To Begin With (1981).

10. Bekker, A., Roux, J. J. J. & Mosteit, P. J. A generalization of the compound rayleigh distribution: Using a bayesian method on cancer survival times. Communications in Statistics- Theory and Methods 29, 1419–1433 (2000). https://doi.org/10.1080/03610920008832554

11. Benrabia, M. & Alzoubi, L. M. A. Alzoubi distribution: Properties and applications. An International Journal of Statistics Applications & Probability 11, 1–16 (2021).

12. Club, T. B. in 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, USSR,

September 2-8, 1971 (eds Petrov, B. N. & Csáki, F.) 267–281 (Akadémiai Kiadó, Budapest, 2016).

13. Dey, S., Ghosh, I. & Kumar, D. Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data. Annals of Data Science 6, 623-650 (2019). https://doi.org/10.1007/s40745-018-0163-2

14. Elbatal, I., Elgarhy, M. & Golam Kibria, B. M. Alpha Power Transformed Weibull-G Family of Distributions: Theory and Applications. Journal of Statistical Theory and Applications 20, 340 (2021). https://doi.org/10.2991/jsta.d.210222.002

15. Elechi, O., Okereke, E. W., Chukwudi, I. H., Chizoba, K. L. & Wale, O. T. Iwueze’s Distribution and Its Application. Journal of Applied Mathematics and Physics 10, Article 12 (2022). https://doi.org/10.4236/jamp.2022.1012251

16. Epstein, N. Exponential Distribution and Its Role in Life Testing pp. 1–21 (1958).

17. Eugene, N., Lee, C. & Famoye, F. Beta-Normal Distribution and Its Applications. Communications in Statistics- Theory and Methods 31, 497–512 (2002). https://doi.org/10.1081/STA-120003130

18. Gomaa, R. S., Hebeshy, E. A., El Genidy, M. M. & El-Desouky, B. S. Alpha-Power of the Power Ailamujia Distribution: Properties and Applications https://www.researchgate.net/profile/Rabab-Sabry/publication/371732162_Alpha-Power_of_the_Power_Ailamujia_Distribution_Properties_and_Applications/links/6492b61dc41fb852dd1bbd22/Alpha- Power of the Power-Ailamujia-Distribution-Properties-and-Applications.pdf. Accessed: [date of access]. 2023.

19. Hassan, A. S., Elgarhy, M., Mohamd, R. E. & Alrajhi, S. On the alpha power transformed power Lindley distribution. Journal of Probability and Statistics. (2019). https://www.hindawi.com/journals/jps/2019/8024769/abs/

20. Hassan, A. S., Mohamd, R. E., Elgarhy, M. & Fayomi, A. Alpha power transformed extended exponential distribution: Properties and applications. Journal of Nonlinear Sciences and Applications 12, 62–67 (2018).

21. Hozaien, H. E., Dayian, G. &EL-Helbawy, A. A. Kumaraswamy Distribution Based on Alpha Power Transformation Methods. Asian Journal of Probability and Statistics 11, 14–29 (2021). https://doi.org/10.9734/AJPAS/2021/v11i130257

22. Jones, M. C. On Families of Distributions with Shape Parameters. International Statistical Review 83, 175–192 (2015). https://doi.org/10.1111/insr.12055

23. Lee, C., Famoye, F. & Alzaatreh, A. Y. Methods for generating families of univariate continuous distributions in the recent decades. WIREs Computational Statistics 5, 219–238 (2013). https://doi.org/10.1002/wics.1255

24. Mahdavi, A. & Kundu, D. A new method for generating distributions with an application to exponential distribution. Communications in Statistics- Theory and Methods 46, 6543–6557 (2016). https://doi.org/10.1080/03610926.2015.1130839

25. Marshall, A. W. & Olkin, I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84, 641–652 (1997).

26. Mead, M. E., Cordeiro, G. M., Afify, A. Z. & Al Mofleh, H. The alpha power transformation family: Properties and applications. Pakistan Journal of Statistics and Operation Research, 525–545 (2019).

27. Mohiuddin, M., Bayatti, H. A. & Kannan, R. A new generalization of Garima distribution with application to real life data. Applied Mathematics & Information Sciences 15, 577–592 (2021).

28. Mohiuddin, M. & Kannan, R. A new generalization of Rama distribution with application to machinery data. International Journal of Emerging Technologies in Engineering Research 9, 1–13 (2021).

29. Mohiuddin, M. & Kannan, R. Alpha power transformed aradhana distributions, its properties and applications. Indian Journal of Science and Technology 14, 2483–2493 (2021).

30. Mohiuddin, M. & Kannan, R. Characterization and Estimation of Alpha Power Sujatha Distribution with Applications to Engineering Data. International Research Journal of Engineering and Technology 9, 1421–1432 (2022).

31. Mohiuddin, M., Kannan, R., Alrashed, A. A. & Fasil, M. A New Generalization of Pranav Distribution with Application to Model Real Life Data. Journal of Statistics Applications & Probability 11, 991–1011 (2022).

32. Mohiuddin, M., Kannan, R., Migdadi, H. S. & Khder, M. On The Alpha Power Transformed Quasi Aradhana Distribution: Properties and Applications. Appl. Math 16, 197–211 (2022).

33. Mudholkar, G. S. & Srivastava, D. K. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42, 299–302 (1993).

34. Nasiru, S., Mwita, P. N. & Ngesa, O. Alpha power transformed Frechet distribution. Applied Mathematics & Information Sciences 13, 129–141 (2019).

35. Nassar, M., Alzaatreh, A., Abo-Kasem, O., Mead, M. & Mansoor, M. A new family of generalized distributions based on alpha power transformation with application to cancer data. Annals of Data Science 5, 421–436 (2018).

36. Pollock, D. S. G., Green, R. C. & Nguyen, T. Handbook of time series analysis, signal processing, and dynamics (Elsevier, 1999).

37. Renyi, A. On measures of entropy and information in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, 547–562. (1961).

38. Ronald, W. E., Myers, R. H., Myers, S. L. & Ye, K. E. Probability and Statistics for Engineers and Scientists, 9th. http://library.lol/main/09C6713DAA3BF89644499A5EB315D12E (Prentice Hall, 2011).

39. Sakthivel, K. M. Alpha power transformed Pareto distribution and its properties with application. Malaya Journal of Matematik (MJM) 1, 52–57 (2020).

40. Shanker, R. Akash Distribution and Its Applications. International Journal of Probability and Statistics 4, 65–75 (2015). https://doi.org/10.5923/j.ijps.20150403.01

41. Shanker, R. Shanker Distribution and Its Applications. International Journal of Statistics and Applications 5, 338–348 (2015).

42. Shanker, R. Sujatha Distribution and its Applications. Statistics in Transition New Series 17, 391-410. https://doi.org/10.21307/stattrans-2016-029 (2016).

43. Shanker, R. & Shukla, K. K. A New Quasi Sujatha Distribution. Statistics in Transition New Series 21, 53–71 (2020).

44. Shannon, C. E. Prediction and entropy of printed English. Bell System Technical Journal 30, 50–64 (1951).

45. Shaw, W. T. & Buckley, I. R. C. The alchemy of probability distributions: Beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv:0901.0434. 2009. http://arxiv.org/abs/0901.0434.

46. Shraa, D. H. & Al-Omari, A. I. Darna distribution: Properties and application. Electronic Journal of Applied Statistical Analysis 12, 520–541 (2019). https://doi.org/10.1285/i20705948v12n2p520

47. Shukla, K. K. Prakaamy distribution with properties and applications. JAQM 13, 30–38 (2018).

48. Shukla, K. K. Ram Awadh distribution with properties and applications. Biometrics & Biostatistics International Journal 7, 515–523 (2018). https://doi.org/10.15406/bbij.2018.07.00254

49. Toomet, O., Henningsen, A. & Toomet, M. O. Package maxLik Software package. 2015.

50. Umeh, E. & Ibenegbu, A. A Two-Parameter Pranav Distribution with Properties and Its Application. Journal of Biostatistics and Epidemiology 5, 74–90 (2019). https://doi.org/10.18502/jbe.v5i1.1909

51. Uwaeme, O. R. & Akpan, N. P. The Remkan Distribution and Its Applications. Asian Journal of Probability and Statistics 26, 13–24 (2024).

52. ZeinEldin, R. A., Ahsan ul Haq, M., Hashmi, S. & Elsehety, M. Alpha power transformed inverse Lomax distribution with different methods of estimation and applications. Complexity, 1–15 (2020).

Similar Articles

<< < 4 5 6 7 8 9 10 11 12 13 14 15 16 > >> 

You may also start an advanced similarity search for this article.