A Novel Lifetime Model With A Bathtub-Shaped Hazard Rate: Properties & Applications

Abdullah H.  Al-nefaie; Ibrahim E.  Ragab

doi:10.6180/jase.202303_26(3).0012

A Novel Lifetime Model With A Bathtub-Shaped Hazard Rate: Properties & Applications

Computer Science and Information Engineering

Abdullah H. Al-nefaie This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Ibrahim E. Ragab²

¹Quantitative Methods Department, School of Business, King Faisal University, Al Ahsa, Saudi Arabia
²Higher Institute of Computer, King Mariout, Alexandria 23713, Egypt

Received: December 28, 2021
Accepted: March 23, 2022
Publication Date: June 17, 2022

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202303_26(3).0012

ABSTRACT

A novel three-parameter lifetime model called the Marshall Olkin power Ailamujia (MOPA) distribution is developed. The statistical qualities and reliability characteristics of the proposed model are examined, including moment, generating function, incomplete moments, mean deviation, Bonferroni, and Lorenz curves. The maximum likelihood technique has been used to investigate the estimate of underlying parameters. Finally, two real-world datasets are utilized to show the model’s applicability.

Keywords: Marshall-Olkin Family; Power Ailamujia; Hazard Rate Function; Moments; Residual Analysis; Maximum Likelihood Estimation

REFERENCES

[1] H. Lv, L. Gao, and C. Chen, (2002) “3 Parameter distribution
and its application in support ability data analysis" Journal of Academy of Armored Force Engineering 16(3): 48–52.
[2] G. Pan, B. Wang, C. Chen, Y. Huang, and M. Dang, (2009) “The research of interval estimation and hypothetical test of small sample of distribution" Application of statistics and management 28(3): 468–472.
[3] L. Bing, (2015) “Bayesian Estimation of Parameter on 3 Parameter Distribution Under Different Prior Distribution" Mathematics in Practice and Theory:
[4] C. Yu, Y. Chi, Z. Zhao, and J. Song, (2015) “Maintancedecision- oriented modeling and emulating of battle field injury in campaign macrocosm" Journal of System Simulation 20(20): 5669–5671.
[5] U. Jan, K. Fatima, and S. Ahmad, (2017) “On weighted Ailamujia distribution and its applications to lifetime data" Journal of statistics Applications and Probability 6(3): 619–633.
[6] F. Jamal, C. Chesneau, K. Aidi, and A. Ali, (2021) “Theory and application of the power ailamujia distribution" Journal of Mathematical Modeling 9(3): 391–413. DOI: 10.22124/jmm.2020.17547.1512.
[7] N. Eugene, C. Lee, and F. Famoye, (2002) “Betanormal distribution and its applications" Communications in Statistics - Theory and Methods 31(4): 497–512. DOI: 10.1081/STA-120003130.
[8] K. Zografos and N. Balakrishnan, (2009) “On families of beta- and generalized gamma-generated distributions and associated inference" Statistical Methodology 6(4): 344–362. DOI: 10.1016/j.stamet.2008.12.003.
[9] G. Cordeiro and M. de Castro, (2011) “A new family of generalized distributions" Journal of Statistical Computation and Simulation 81(7): 883–898. DOI: 10.1080/00949650903530745.
[10] C. Alexander, G. Cordeiro, E. Ortega, and J. Sarabia, (2012) “Generalized beta-generated distributions" Computational Statistics and Data Analysis 56(6): 1880–1897. DOI: 10.1016/j.csda.2011.11.015.
[11] R. R. Pescim, E. M. Ortega, G. M. Cordeiro, C. G.
Demtrio, and G. Hamedani, (2013) “The log-beta generalized
half-normal regression model" Journal of Statistical Theory and Applications:
[12] S. Nadarajah, G. Cordeiro, and E. Ortega, (2015) “The zografos-balakrishnan-G family of distributions: Mathematical properties and applications" Communications in Statistics - Theory and Methods 44(1): 186–215. DOI: 10.1080/03610926.2012.740127.
[13] E. Ortega, A. Lemonte, G. Silva, and G. Cordeiro, (2015) “New flexible models generated by gamma random variables for lifetime modeling" Journal of Applied Statistics 42(10): 2159–2179. DOI: 10.1080/02664763.2015.1021669.
[14] A. Marshall and I. Olkin, (1997) “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families" Biometrika 84(3): 641–652. DOI: 10.1093/biomet/84.3.641.
[15] M. Ghitany, E. Al-Hussaini, and R. Al-Jarallah, (2005) “Marshall-Olkin extended Weibull distribution and its application to censored data" Journal of Applied Statistics 32(10): 1025–1034. DOI: 10.1080/02664760500165008.
[16] I. E. Okorie, A. C. Akpanta, and J. Ohakwe, (2017) “Marshall-Olkin generalized Erlang-truncated exponential distribution: Properties and applications" Cogent Mathematics 4(1): 1285093.
[17] K. Jayakumar and T. Mathew, (2008) “On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution" Statistical Papers 49(3): 421–439. DOI: 10.1007/s00362-006-0024-5.
[18] K. Jose, S. Naik, and M. Risti´c, (2010) “Marshall-Olkin q-Weibull distribution and max-min processes" Statistical Papers 51(4): 837–851. DOI: 10.1007/s00362-008-0173-9.
[19] M. Pérez-Casany and A. Casellas, (2013) “Marshall-Olkin Extended Zipf Distribution" arXiv preprint arXiv:1304.4540:
[20] E. Krishna, K. Jose, T. Alice, and M. Risti´c, (2013) “The marshall-olkin fréchet distribution" Communications in Statistics - Theory and Methods 42(22): 4091–4107. DOI: 10.1080/03610926.2011.648785.
[21] W. Gui, (2013) “A Marshall-Olkin power log-normal distribution and its applications to survival data" International Journal of Statistics and Probability 2(1):63.
[22] P. Gupta and R. Gupta, (1983) “On the moments of residual life in reliability and some characterization results" Communications in Statistics - Theory and Methods 12(4): 449–461. DOI: 10.1080/03610928308828471.
[23] C.-D. Lai and M. Xie. Stochastic ageing and dependence for reliability. Cited by: 480. 2006, 1–418. DOI: 10.1007/0-387-34232-X.
[24] F. Guess and F. Proschan, (1988) “12 Mean residual life: Theory and applications" Handbook of Statistics 7: 215–224. DOI: 10.1016/S0169-7161(88)07014-2.
[25] J. Navarro, Y. del Aguila, and M. Asadi, (2010) “Some new results on the cumulative residual entropy" Journal of Statistical Planning and Inference 140(1): 310–322. DOI: 10.1016/j.jspi.2009.07.015.
[26] A. Rényi. “On measures of entropy and information”. In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. 4. University of California Press. 1961, 547–562.
[27] X. K., X. M., T. L.C., and H. S.L., (2003) “Application of neural networks in forecasting engine systems reliability" Applied Soft Computing Journal 2(4): 255–268. DOI: 10.1016/S1568-4946(02)00059-5.
[28] R. L. Smith and J. Naylor, (1987) “A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution" Journal of the Royal Statistical Society: Series C (Applied Statistics) 36(3): 358–369.
[29] M. Risti´c and D. Kundu, (2015) “Marshall-Olkin generalized exponential distribution" Metron 73(3): 317–333. DOI: 10.1007/s40300-014-0056-x.
[30] M. Mansoor, M. Tahir, G. Cordeiro, S. Provost, and A. Alzaatreh, (2019) “The Marshall-Olkin logistic exponential distribution" Communications in Statistics - Theory and Methods 48(2): 220–234. DOI: 10.1080/03610926.2017.1414254.
[31] M. Aarset, (1987) “How to Identify a Bathtub Hazard Rate" IEEE Transactions on Reliability R-36(1): 106–108. DOI: 10.1109/TR.1987.5222310.