Journal of applied mathematics & informatics

  • 제41권6호
  • /
  • Pages.1275-1301
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  • 2023
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A NOVEL WEIBULL MARSHALL-OLKIN POWER LOMAX DISTRIBUTION: PROPERTIES AND APPLICATIONS TO MEDICINE AND ENGINEERING

  • ELHAM MORADI (Department of Statistics and Mathematics, Central Tehran Branch, Islamic Azad University) ;
  • ZAHRA SHOKOOH GHAZANI (Department of Statistics and Mathematics, Central Tehran Branch, Islamic Azad University)
  • 투고 : 2022.12.29
  • 심사 : 2023.09.12
  • 발행 : 2023.11.30
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초록

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

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과제정보

The authors would like to thank referees for useful comments and suggestions.

참고문헌

  1. I.B. Abdul-Moniem, Statistics recurrence relations for moments of lower generalized order from exponentiated Lomax distribution and its characterization, J. Math. Comput. Sci. 2 (2012), 999-1011. 
  2. M. Ahsanullah, Record values of the Lomax distribution, Statistica Neerlandica 45 (1991), 21-29.  https://doi.org/10.1111/j.1467-9574.1991.tb01290.x
  3. M. Alizadeh and et al., The beta Marshall-Olkin family of distributions, Journal of Statistical Distributions and Applications 2 (2015), 1-18.  https://doi.org/10.1186/s40488-014-0024-2
  4. A.M. Almarashi, Truncated Cauchy Power Lomax Model and Its Application to Biomedical Data, Nanoscience and Nanotechnology Letters 12 (2020), 16-24.  https://doi.org/10.1166/nnl.2020.3080
  5. S. Al-Marzouki and et al., Type II Topp Leone power Lomax distribution with applications, Mathematics 8 (2019), 4. 
  6. S. Al-Marzouki, Truncated Weibull power Lomax distribution statistical properties and applications, Journal of Nonlinear Sciences & Applications (JNSA) 12 (2019). 
  7. H.M. Almongy, E.M. Almetwally and A.E. Mubarak, Marshall-Olkin alpha Power lomax distribution: Estimation methods, applications on physics and economics, Pakistan Journal of Statistics and Operation Research (2021), 137-153. 
  8. A. Alzaatreh, C. Lee and F. Famoye, A new method for generating families of continuous distributions, Metron 71 (2013), 63-79.  https://doi.org/10.1007/s40300-013-0007-y
  9. S. Ashour and M. Eltehiwy, Transmuted exponentiated Lomax distribution, Australian Journal of Basic and Applied Sciences 7 (2013), 658-667. 
  10. M. Atkinson and A.J. Harrison, Personal Wealth in Britan, CUP Archive, 1978. 
  11. M.C. Bryson, Heavy-tailed distributions: properties and tests, Technometrics 16 (1974), 61-68.  https://doi.org/10.1080/00401706.1974.10489150
  12. Y.M. Bulut, F.Z. Do˘gru and O. Arslan, Alpha power Lomax distribution: Properties and application, Journal of Reliability and Statistical Studies (2021), 17-32. 
  13. A. Corbellini and et al., Fitting Pareto II distributions on firm size: Statistical methodology and economic puzzles, Advances in Data Analysis: Theory and Applications to Reliability and Inference, Data Mining, Bioinformatics, Lifetime Data, and Neural Networks, (2010), 321-328. 
  14. G.M. Cordeiro, E.M. Ortega and B.V. Popovic, The gamma-Lomax distribution, Journal of Statistical computation and Simulation 85 (2015), 305-319.  https://doi.org/10.1080/00949655.2013.822869
  15. G.M. Cordeiro, E.M.M. Ortega and T.G. Ramires, A new generalized Weibull family of distributions: mathematical properties and applications, Journal of Statistical Distributions and Applications 2 (2015), 1-25.  https://doi.org/10.1186/s40488-014-0024-2
  16. E. Cramer and A.B. Schmiedt, Progressively type-II censored competing risks data from Lomax distributions, Computational Statistics & Data Analysis 55 (2011), 1285-1303.  https://doi.org/10.1016/j.csda.2010.09.017
  17. M.M.E.A. El-Monsef, N.H. Sweilam and M.A. Sabry, The exponentiated power Lomax distribution and its applications, Quality and Reliability Engineering International 37 (2021), 1035-1058.  https://doi.org/10.1002/qre.2780
  18. P. Flajolet and R. Sedgewick, Analytic combinatorics, Cambridge University press, 2009. 
  19. Z.S. Ghazani, Symmetrization procedures for the law of the iterated logarithm, Journal of Mathematical Analysis 12 (2021), 44-53. 
  20. M. Ghitany, F. Al-Awadhi and L. Alkhalfan, Marshall-Olkin extended Lomax distribution and its application to censored data, Communications in Statistics-Theory and Methods 36 (2007), 1855-1866.  https://doi.org/10.1080/03610920601126571
  21. J. Gillariose and L. Tomy, The Marshall-Olkin extended power lomax distribution with applications, Pakistan Journal of Statistics and Operation Research (2020), 331-341. 
  22. R.C. Gupta, M. Ghitany and D. Al-Mutairi, Estimation of reliability from Marshall-Olkin extended Lomax distributions, Journal of Statistical Computation and Simulation 80 (2010), 937-947.  https://doi.org/10.1080/00949650902845672
  23. A.S. Hassan and A.S. Al-Ghamdi, Optimum step stress accelerated life testing for Lomax distribution, Journal of Applied Sciences Research 5 (2009), 2153-2164. 
  24. A.S. Hassan and et al., Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples, Pakistan Journal of Statistics and Operation Research (2021), 343-356. 
  25. A.S. Hassan and M. Abd-Allah, On the inverse power Lomax distribution, Annals of Data Science 6 (2019), 259-278.  https://doi.org/10.1007/s40745-018-0183-y
  26. A.S. Hassan, M. Sabry and A. Elsehetry, Truncated power Lomax distribution with application to flood data, J. Stat. Appl. Prob. 9 (2020), 347-359.  https://doi.org/10.18576/jsap/090214
  27. O. Holland, A. Golaup and A. Aghvami, Traffic characteristics of aggregated module downloads for mobile terminal reconfiguration, IEE Proceedings-Communications 153 (2006), 683-690.  https://doi.org/10.1049/ip-com:20045155
  28. N.A. Hussain, S. Doguwa and A. Yahaya, The Weibull-Power Lomax Distribution: Properties and Application, Communication in Physical Sciences 6 (2020). 
  29. S. Ibrahim and et al., Some Properties and Applications of Topp Leone Kumaraswamy Lomax Distribution, Journal of Statistical Modeling & Analytics (JOSMA) 3 (2021). 
  30. M.C, . Korkmaz and et al., The Weibull Marshall-Olkin family: Regression model and application to censored data, Communications in Statistics-Theory and Methods 48 (2019), 4171-4194.  https://doi.org/10.1080/03610926.2018.1490430
  31. K. Kwan and et al., Kinetics of indomethacin absorption, elimination, and enterohepatic circulation in man, Journal of Pharmacokinetics and Biopharmaceutics 4 (1976), 255-280.  https://doi.org/10.1007/BF01063617
  32. A.J. Lemonte and G.M. Cordeiro, An extended Lomax distribution, Statistics 47 (2013), 800-816.  https://doi.org/10.1080/02331888.2011.568119
  33. A.W. Marshall and I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika 84 (1997), 641-652.  https://doi.org/10.1093/biomet/84.3.641
  34. T. Moltok, H. Dikko and O. Asiribo, A transmuted Power Lomax distribution, African Journal of Natural Sciences (AJNS) 20 (2019). 
  35. D.P. Murthy, M. Xie and R. Jiang, Weibull models, John Wiley & Sons, 2004. 
  36. J. Myhre and S. Saunders, Screen testing and conditional probability of survival, Lecture Notes-Monograph Series (1982), 166-178. 
  37. V.B. Nagarjuna, R.V. Vardhan and C. Chesneau, Kumaraswamy generalized power lomax distributionand its applications, Stats. 4 (2021), 28-45.  https://doi.org/10.3390/stats4010003
  38. V.B. Nagarjuna, R.V. Vardhan and C. Chesneau, On the accuracy of the sine Power lomax model for data fitting, Modelling 2 (2021), 78-104.  https://doi.org/10.3390/modelling2010005
  39. E.E. Nwezza and F.I. Ugwuowo, The Marshall-Olkin Gumbel-Lomax distribution: properties and applications, Heliyon 6 (2020), 03569. 
  40. A.A. Ogunde and et al., Harris Extended Power Lomax Distribution: Properties, Inference and Applications, International Journal of Statistics and Probability 10 (2021), 1-77. 
  41. I. Okorie and et al., The modified power function distribution, Cogent mathematics 4 (2017), 1319592. 
  42. B. Punathumparambath, Estimation of P(X > Y ) for the double Lomax distribution, In Probstat forum, 2011. 
  43. E.-H.A. Rady, W. Hassanein and T. Elhaddad, The power Lomax distribution with an application to bladder cancer data, SpringerPlus 5 (2016), 1-22.  https://doi.org/10.1186/s40064-015-1659-2
  44. M. Rajab and et al., On five parameter beta Lomax distribution, Journal of Statistics 20 (2013). 
  45. M.W.A. Ramos and et al., The exponentiated Lomax Poisson distribution with an application to lifetime data, Advances and Applications in Statistics 34 (2013), 107. 
  46. N. Singla, K. Jain and S.K. Sharma, The beta generalized Weibull distribution: properties and applications, Reliability Engineering & System Safety 102 (2012), 5-15.  https://doi.org/10.1016/j.ress.2012.02.003
  47. M.A. Ul Haq and et al., Marshall-Olkin power Lomax distribution for modeling of wind speed data, Energy Reports 6 (2020), 1118-1123. https://doi.org/10.1016/j.egyr.2020.04.033