Communications for Statistical Applications and Methods

  • 제28권2호
  • /
  • Pages.99-118
  • /
  • 2021
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Parameter estimation of an extended inverse power Lomax distribution with Type I right censored data

  • Hassan, Amal S. (Department of Mathematical Statistics, Cairo University) ;
  • Nassr, Said G. (Department of Quantitative Methods, Sinai University)
  • 투고 : 2019.12.24
  • 심사 : 2021.01.08
  • 발행 : 2021.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

키워드

과제정보

The authors are grateful to the editor and referees for their useful comments and suggestions for improvement which undoubtedly enhanced the presentation and quality of the article.

참고문헌

  1. Abdul-Moniem IB and Abdel-Hameed HF (2012). A lifetime distribution with decreasing failure rate, International Electronic Journal of Mathematics Education, 33, 1-7.
  2. Al-Marzouk S, Jamal F, Chesneau C, and Elgarhy M (2020). Type II Topp Leone power Lomax distribution with applications, Mathematics, 8, 1-26. https://doi.org/10.3390/math8010001
  3. Atkinson AB and Harrison A (1978). Distribution of Personal Wealth in Britain, Cambridge University Press, Cambridge.
  4. Bantan R, Hassan AS, and Elsehetry M (2020). Generalized Marshall Olkin Inverse Lindley Distribution with Applications, Computers, Materials, Continua, 64, 1505-1526. https://doi.org/10.32604/cmc.2020.010887
  5. Bjerkedal T (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli, American Journal of Hygiene, 72, 130-148.
  6. Cordeiro GM, Ortega E, and Popovic B (2013). The gamma Lomax distribution, ' Journal of Statistical Computation and Simulation, 85, 305-319. https://doi.org/10.1080/00949655.2013.822869
  7. Ghitany ME, AL-Awadhi FA, and Alkhalfan LA (2007). Marshall-Olkin extended Lomax distribution and its applications to censored data, Communications in Statistics: Theory and Methods, 36, 1855-1866. https://doi.org/10.1080/03610920601126571
  8. Haq MA, Hamedani GG, Elgarhy M, and Ramos PL (2020). Marshall-Olkin power Lomax distribution: properties and estimation based on complete and censored samples, International Journal of Statistics and Probability, 9, 48-62. https://doi.org/10.5539/ijsp.v9n1p48
  9. Harris CM (1968). The Pareto distribution as a queue service discipline, Operational Research, 16, 307-313. https://doi.org/10.1287/opre.16.2.307
  10. Hassan A, Ascsar S, and Shelbaia A (2016). Optimum step stress accelerated life test plan for Lomax distribution with an adaptive type-II progressive hybrid censoring, British Journal of Mathematics Computer Science, 13, 1-19.
  11. Hassan AS and Abd-Allah M (2017). Exponentiated Lomax geometric distribution: properties and applications, Pakistan Journal of Statistics and Operation Research, 13, 545-566. https://doi.org/10.18187/pjsor.v13i3.1437
  12. Hassan AS and Abd-Allah M (2018). Exponentiated Weibull-Lomax distribution: properties and estimation, Journal of Data Science, 16, 277-298.
  13. Hassan AS and Abd-Allah M (2019). On the inverse power Lomax distribution, Annals of Data Science, 6, 259-278. https://doi.org/10.1007/s40745-018-0183-y
  14. Hassan AS and Al-Ghamdi A (2009). Optimum step stress accelerated life testing for Lomax distribution, Journal of Applied Sciences Research, 5, 2153-2164.
  15. Hassan AS, Elgarhy M, and Mohamed RE (2020). Statistical properties and estimation of type II half logistic Lomax distribution, Thailand Statistician, 18, 290-305.
  16. Hassan AS and Mohamed RE (2019). Parameter estimation for inverted exponentiated Lomax distribution with right censored data, Gazi University Journal of Science, 32, 1370-1386. https://doi.org/10.35378/gujs.452885
  17. Hassan AS and Mohamed RE (2019). Weibull inverse Lomax distribution right censored data, Pakistan Journal of Statistics and Operation Research, 15, 587-603. https://doi.org/10.18187/pjsor.v15i3.2378
  18. Hassan AS and Nassr SG (2018). Power Lomax Poisson distribution: properties and estimation, Journal of Data Science, 18, 105-128.
  19. Hassan AS, Sabry MAS, and Elsehetry A (2020). Truncated power Lomax distribution with application to flood data, Journal of Statistics Applications Probability, 9, 347-359. https://doi.org/10.18576/jsap/090214
  20. Holland O Golaup A, and Aghvami AH (2006). Traffic characteristics of aggregated module downloads for mobile terminal reconfiguration, IEE Proceedings Communications, 153, 683-690. https://doi.org/10.1049/ip-com:20045155
  21. Krishna E, Jose KK, Alice T, and Ristic MM (2013). The Marshall-Olkin Fr ' echet distribution, ' Communications in Statistics: Theory and Methods, 42, 4091-4107. https://doi.org/10.1080/03610926.2011.648785
  22. Lemonte AJ and Cordeiro GM (2013). An extended Lomax distribution, Statistics, 47, 800-816. https://doi.org/10.1080/02331888.2011.568119
  23. Marshall AW and Olkin I (1997). A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families, Biometrika, 84, 641-52. https://doi.org/10.1093/biomet/84.3.641
  24. M-Gharib, Mohammed BI, and Aghel WER (2017). Marshll-Olkin extended inverse Pareto distribution and its application, International Journal of Statistics and Probability, 6, 71-84. https://doi.org/10.5539/ijsp.v6n6p71
  25. Murthy DNP, Xie M, and Jiang R (2004). Weibull Models, Series in Probability And Statistics, John Wiley, New Jersey.
  26. Pogany TK, Saboor A, and Provost S (2015). The Marshall-Olkin exponential Weibull distribution, ' Hacettepe Journal of Mathematics and Statistics, 44, 1579-1594.
  27. Rady EA, Hassanein WA, and Elhaddad TA (2016). The power Lomax distribution with an application to bladder cancer data, SpringerPlus, 5, 1838. https://doi.org/10.1186/s40064-016-3464-y
  28. Rao GS, Ghitany ME, and Kantam RRL (2009). Marshall-Olkin extended Lomax distribution: an economic reliability test plan, International Journal Of Applied Mathematics, 22, 139-148.
  29. Shaked M and Shanthikumar J (1994). Stochastic Orders and Their Applications, Academic Press, Boston
  30. Tahir M Cordeiro GM Mansoor M, and Zubair M (2015). The Weibull-Lomax distribution: properties and applications, Hacettepe Journal of Mathematics and Statistics, 44, 461-480.
  31. Tahir MH, Hussain MA, Cordeiro GM, Hamedani GG, Mansoor M, and Zubair M (2016). The Gumbel-Lomax distribution: properties and applications, Journal of Statistical Theory and Applic ations, 15, 61-79. https://doi.org/10.2991/jsta.2016.15.1.6