On Some Properties of a New Truncated Model With Applications to Lifetime Data

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Muhammad Zeshan Arshad
Oluwafemi Samson Balogun
Muhammad Zafar Iqbal
Pelumi E. Oguntunde

Abstract

This research explored the exponentiated left truncated power distribution which is a bounded model. Various statistical properties which include the moments and their associated measures, Bonferroni and Lorenz curves, reliability measures, shapes, quantile function, entropy, and order statistics were discussed in detail. A simulation study was provided and applications to two real-world data were considered. The performance of the exponentiated left truncated power distribution over other bounded models like Topp-Leone distribution, Beta distribution, Kumaraswamy distribution, Lehmann type–I distribution, Lehmann type–II distribution, generalized power function, Weibull power function, and Mustapha type–II distribution is quite commendable.

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References

  1. M. Ahsan-ul-Haq, M. Ahmed, J. Zafar, P.L. Ramos, Modeling of COVID-19 cases in Pakistan using lifetime probability distributions, Ann. Data. Sci. 9 (2022), 141–152. https://doi.org/10.1007/s40745-021-00338-9.
  2. A. Al Mutair, A. Al Mutairi, Y. Alabbasi, A. Shamsan, S. Al-Mahmoud, S. Alhumaid, M. zeshan Arshad, M. Awad, A. Rabaan, Level of anxiety among healthcare providers during COVID-19 pandemic in Saudi Arabia: cross-sectional study, PeerJ. 9 (2021), e12119. https://doi.org/10.7717/peerj.12119.
  3. A. Al Mutairi, M.Z. Iqbal, M.Z. Arshad, B. Alnssyan, H. Al-Mofleh, A.Z. Afify, A new extended model with bathtub-shaped failure rate: Properties, inference, simulation, and applications, Mathematics. 9 (2021), 2024. https://doi.org/10.3390/math9172024.
  4. A. Al-Shomrani, O. Arif, A. Shawky, S. Hanif, M.Q. Shahbaz, Topp–Leone family of distributions: Some properties and application, Pak. J. Stat. Oper. Res. 12 (2016), 443. https://doi.org/10.18187/pjsor.v12i3.1458.
  5. S. Arimoto, Information-theoretical considerations on estimation problems, Inform. Control. 19 (1971), 181–194. https://doi.org/10.1016/S0019-9958(71)90065-9.
  6. O.S. Balogun, M.Z. Arshad, M.Z. Iqbal, M. Ghamkhar, A new modified Lehmann type – II G class of distributions: exponential distribution with theory, simulation, and applications to engineering sector, F1000Res. 10 (2021), 483. https://doi.org/10.12688/f1000research.52494.1.
  7. D.E. Boekee, J.C.A. Van der Lubbe, The R-norm information measure, Inform. Control. 45 (1980), 136– 155. https://doi.org/10.1016/S0019-9958(80)90292-2.
  8. G.M. Cordeiro, M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2011), 883–898. https://doi.org/10.1080/00949650903530745.
  9. N. Eugene, C. Lee, F. Famoye, Beta-normal distribution and its applications, Commun. Stat. – Theory Methods. 31 (2002), 497–512. https://doi.org/10.1081/STA-120003130.
  10. M.D.P. Esberto, Probability distribution fitting of rainfall patterns in Philippine regions for effective risk management, Environ. Ecol. Res. 6 (2018), 178–186. https://doi.org/10.13189/eer.2018.060305.
  11. H.D. Kan, B.H. Chen, Statistical distributions of ambient air pollutants in Shanghai, China, Biomed. Environ. Sci. 17(3) (2004), 366-272. https://pubmed.ncbi.nlm.nih.gov/15602835/.
  12. P. Kumaraswamy, A generalized probability density function for double-bounded random processes, J. Hydrol. 46 (1980), 79–88. https://doi.org/10.1016/0022-1694(80)90036-0.
  13. R.J. Hyndman, Y. Fan, Sample quantiles in statistical packages, Amer. Stat. 50 (1996), 361–365. https://doi.org/10.1080/00031305.1996.10473566.
  14. J. Havrda, F. Charvat, Quantification method of classification processes. Concept of structural α−entropy. Kybernetika, 3 (1967), 30-35.
  15. E.L. Lehmann, The power of rank tests, Ann. Math. Statist. 24 (1953) 23–43. https://doi.org/10.1214/aoms/1177729080.
  16. K. Modi, V. Gill, Unit Burr-III distribution with application, J. Stat. Manage. Syst. 23 (2020), 579–592. https://doi.org/10.1080/09720510.2019.1646503.
  17. J. Mazucheli, A.F. Menezes, M.E. Ghitany. The unit-Weibull distribution and associated inference, J. Appl. Probab. Stat. 13(2018), 1-22.
  18. A. Mathai, H. Haubold, On a generalized entropy measure leading to the pathway model with a preliminary application to solar neutrino data, Entropy. 15 (2013), 4011–4025. https://doi.org/10.3390/e15104011.
  19. M. Muhammad, A new lifetime model with a bounded support, Asian Res. J. Math. 7 (2017), ARJOM.35099. https://doi.org/10.9734/ARJOM/2017/35099.
  20. D.N.P. Murthy, M. Xie, R. Jiang, Weibull models, J. Wiley, Hoboken, N.J, 2004.
  21. S. Nasiru, A.G. Abubakari, I.D. Angbing, Bounded odd inverse pareto exponential distribution: Properties, estimation, and regression, Int. J. Math. Math. Sci. 2021 (2021), 9955657. https://doi.org/10.1155/2021/9955657.
  22. P.E. Oguntunde, O.A. Odetunmibi, A.O. Adejumo, A study of probability models in monitoring environmental pollution in Nigeria, J. Probab. Stat. 2014 (2014), 864965. https://doi.org/10.1155/2014/864965.
  23. C.P. Quesenberry, C. Hales, Concentration bands for uniformity plots, J. Stat. Comput. Simul. 11 (1980), 41–53. https://doi.org/10.1080/00949658008810388.
  24. A. Rényi. On measures of entropy and information, In: Proceedings of the 4th Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, (1961), 547- 561.
  25. Y. Sangsanit, S.P. Ahmad. The Topp-Leone generator of distributions: properties and inferences. Songklanakarin J. Sci. Technol. 38 (2016), 537-548.
  26. J. Saran, A. Pandey, Estimation of parameters of a power function distribution and its characterization by k-th record values, Statistica. 64 (2004), 523-536. https://doi.org/10.6092/ISSN.1973-2201/56.
  27. C.W. Topp, F.C. Leone, A family of J-shaped frequency functions, J. Amer. Stat. Assoc. 50 (1955), 209– 219. https://doi.org/10.1080/01621459.1955.10501259.
  28. M. Alizadeh, M. Mansoor, G.M. Cordeiro, M. Zubair, M.H. Tahir, The Weibull-power function distribution with applications, Hacettepe J. Math. Stat. 45 (2016), 245-265. https://doi.org/10.15672/HJMS.2014428212.
  29. C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52 (1988), 479–487. https://doi.org/10.1007/BF01016429.
  30. A. Zaharim, S. Najid, A. Razali, K. Sopian. Analyzing Malaysian wind speed data using statistical distribution, In: Proceedings of the 4th IASME/WSEAS International Conference on Energy and Environment (EE ’09), Cambridge, UK (2009), 363-370.