DOI QR코드

DOI QR Code

THE LENGTH-BIASED POWERED INVERSE RAYLEIGH DISTRIBUTION WITH APPLICATIONS

  • MUSTAFA, ABDELFATTAH (Mathematics Department, Faculty of Science, Mansoura University) ;
  • KHAN, M.I. (Mathematics Department, Faculty of Science, Islamic University of Madinah)
  • 투고 : 2021.04.06
  • 심사 : 2021.05.31
  • 발행 : 2022.01.30

초록

This article introduces a new distribution called length-biased powered inverse Rayleigh distribution. Some of its statistical properties are derived. Maximum likelihood procedure is applied to report the point and interval estimations of all model parameters. The proposed distribution is also applied to two real data sets for illustrative purposes.

키워드

과제정보

The researchers wish to extend their sincere gratitude to the Deanship of Scientific Research at the Islamic University of Madinah for the support provided to the Post-Publishing Program 1.

참고문헌

  1. A. Afaq, S.P. Ahmad and A. Ahmed, Length-biased weighted Lomax distribution statistical properties and application, Pakistan Journal of Statistics and Operation Research 12 (2016), 245-255. https://doi.org/10.18187/pjsor.v12i2.1178
  2. M. Ajami and S.M.A. Jahanshahi, Parameter estimation in weighted Rayleigh distribution, Journal of Modern Applied Statistical Methods 16 (2017), 256-276. https://doi.org/10.22237/jmasm/1509495240
  3. A.K. Al-Khadim and A.N. Hussein, New proposed length-biased weighted exponential and Rayleigh distribution with application, Mathematical Theory and Modeling 4 (2014), 137-152.
  4. C. Bonferroni, Elementi di Statistica Generale, Firenze: Seeber, 1930.
  5. G.E.P. Box and D.R. Cox, An analysis of transformations, Journal of the Royal Statistical Society, Series B 26 (1964), 211-252.
  6. D.R. Cox, Renewal Theory, Barnes & Noble, New York, 1962.
  7. K.K. Das and T.D. Roy, Applicability of length biased generalized Rayleigh distribution, Advances in Applied Science Research 2 (2011), 320-327.
  8. K.K. Das and T.D. Roy, On some length-biased weighted Weibull distribution, Advances in Applied Science Research 2 (2011), 465-475.
  9. K. Fatima and S.P. Ahmad, Weighted inverse Rayleigh distribution, International Journal of Statistics and Systems 12 (2017), 119-137.
  10. R.C. Gupta and J.P. Keating, Relations for reliability measures under length biased sampling, Scandanavian Journal of Statistics 13 (1985), 49-56.
  11. P.L. Gupta and R.C. Tripathi, Effect of length-biased sampling on the modeling error, Communications Statistics-Theory and Methods 19 (1990), 1483-1491. https://doi.org/10.1080/03610929008830274
  12. A.J. Gross and V.A. Clark, Survival Distributions: Reliability Applications in the Biometrical Sciences, John Wiley, New York, 1975.
  13. J. Kersey and B.O. Oluyede, Theoretical properties of the length-biased inverse Weibull distribution, Mathematical Sciences Publishers 5 (2012), 379-392.
  14. R. Khattree, Characterization of inverse-Gaussian and gamma distributions through their length-biased distributions, IEEE Transactions on Reliability 38 (1989), 610-611. https://doi.org/10.1109/24.46490
  15. J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd Edition, Wiley, Canada, 2003.
  16. K.A. Mir, A. Ahmed and J.A. Reshi, Structural properties of length biased Beta distribution of first kind, American Journal of Engineering Research 2 (2013), 01-06.
  17. K. Modi, Length-biased weighted Maxwell distribution, Pakistan Journal of Statistics and Operation Research 11 (2015), 465-472. https://doi.org/10.18187/pjsor.v11i4.1008
  18. S. Mudasir and S.P. Ahmad, Structural properties of length liased Nakagami distribution, International Journal of Modern Mathematical Sciences 13 (2015), 217-227.
  19. S. Mudasir and S.P. Ahmad, Characterization and estimation of the length biased Nakagami distribution, Pakistan Journal of Statistics and Operation Research 14 (2018), 697-715. https://doi.org/10.18187/pjsor.v14i3.1930
  20. N. Nanuwong and W. Bodhisuwan, Length biased beta Pareto distribution and its structural properties with application, Journal of Mathematics and Statistics 10 (2014), 49-57. https://doi.org/10.3844/jmssp.2014.49.57
  21. J.M.A. Nashaat, Estimation of two parameter powered inverse Rayleigh distribution, Pakistan Journal of Statistics 36 (2020), 117-133.
  22. B.O. Oluyede, On inequalities and selection of experiments for length-biased distributions, Probability in the Engineering and Informational Sciences 13 (1999), 169-185. https://doi.org/10.1017/s0269964899132030
  23. Z. Praveen and M. Ahmad, Some properties of size - biased weighted Weibull distribution, International Journal of Advanced and Applied Sciences 5 (2018), 92-98. https://doi.org/10.21833/ijaas.2018.12.011
  24. M.V. Ratnaparkhi and U.V. Naik-Nimbalkar, The length biased lognormal distribution and its application in the analysis of data from oil field exploration studies, Journal of Modern Applied Statistical Methods 11 (2012), 225-260.
  25. J.W.S. Rayleigh, On the resultant of a large number of vibrations of the same pitch and of arbitrary phase, Philosophical Magazine, 5th Series 10 (1880), 73-78. https://doi.org/10.1080/14786448008626893
  26. A. Saghir, S. Tazeem and I. Ahmad, The length-biased weighted exponentiated inverted Weibull distribution, Cogent Mathematics 3 (2016), DOI: 10.1080/23311835.2016.1267299.
  27. A. Saghir, A. Khadim and Z. Lin, The Maxwell -length-biased distribution: Properties and estimation, Journal of Statistical Theory and Practice 11 (2017), 26-40. https://doi.org/10.1080/15598608.2016.1246266
  28. P. Seenoi, T. Supapakorn and W. Bodhisuwan, The length-biased exponentiated inverted Weibull distribution, International Journal of Pure and Applied Mathematics 92 (2014), 191-206.
  29. S.A. Shaban and N.A. Boudrissa, The Weibull length-biased distribution: Properties and estimation, Interstat, (2007), http://interstat.statjournals.net/YEAR/2007/articles/0701002.pdf
  30. M.S. Tabass, G.R.M. Borzadaran and M. Amini, Renyi entropy in continuous case is not the limit of discrete case, Mathematical Sciences and Applications E-Notes 4 (2016), 113-117. https://doi.org/10.36753/mathenot.421418
  31. V.N. Trayer, Proceedings of the Academy of Science Belarus, USSR, 1964.
  32. V.G.H. Voda, On the inverse Rayleigh distributed random variable, Rep. Statistics Application and Research, JUSE 19 (1972), 13-21.
  33. K. Xu, M. Xie, L.C. Tang, and S.L. Ho, Application of neural networks in forecasting engine system reliability, Applied Soft Computing 2 (2003), 255-268. https://doi.org/10.1016/S1568-4946(02)00059-5