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Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method

Year 2022, , 1084 - 1092, 31.12.2022
https://doi.org/10.16984/saufenbilder.1137262

Abstract

Important distributions used to model and analyse data in various real-life sciences such as natural sciences, engineering, and medicine are the Weibull, Weibull exponential, and Weibull Rayleigh distribution. The main objective of this paper is to determine the best evaluators and compare them for the distribution with three-parameters of Weibull, Weibull Rayleigh and Exponential Weibull. The methods under consideration for comparing the parameter estimators for these distributions is that of maximum likelihood using the statistical program R for the application of real data. Based on the results obtained from this study, the maximum likelihood approach used in estimating the parameters is the comparison between these distributions.

References

  • [1] G. T. Basheer, Z. Y. Algamal, “Reliability Estimation of Three Parameters Weibull Distribution based on Particle Swarm Optimization”, Pakistan Journal of Statistics and Operation Research, vol. 17, pp. 35-42, 2021.
  • [2] A. M. Abd Elfattah, A. S. Hassanand, D.M. Ziedan, “Efficiency of Maximum Likelihood Estimators under Different Censored Sampling Schemes for Rayleigh Distribution”, Interstat, 2006.
  • [3] R. D. Gupta, D. Kundu, “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrika Journal, vol. 43, pp. 117-130, 2001.
  • [4] E. K. AL-Hussaini, M. Ahsanullah, “Exponentiated Distributions”, Springer, vol. 5, 2015.
  • [5] G. S. Mudholkar, A. D. Hustson, “The exponentiated Weibull family: some properties and a flood data application”, Communications in Statistics-Theory and Methods, vol 25, pp. 3059-3083, 1996.
  • [6] K. Cooray, “Generalization of the Weibull distribution: the odd Weibull family”, Statistical Modelling, vol. 6, pp. 265-277, 2006.
  • [7] B. Marcelo, R. B. Silva , G. Cordeiro, “The Weibull - G Family of Probability Distributions”. Journal of Data Science, vol. 12, pp. 53-68, 2014.
  • [8] W. Barreto-Souza, A.H.S. Santos, G.M. Cordeiro, “The beta generalized exponential distribution”, Journal of Statistical Computation and Simulation, vol. 80, pp. 159-172, 2010.
  • [9] W. Barreto-Souza, A. L. Morais, G.M. Cordeiro, “The Weibull-geometric distribution”, Journal of Statistical Computation and Simulation, vol. 81, pp. 645-657, 2011.
  • [10] A. L. Morais, W. Barreto-Souza, “A compound class of Weibull and power series distributions”, Computational Statistics and Data Analysis, vol. 55, pp. 1410-1425, 2011.
  • [11] A. Choudhury, “A Simple derivation of moments of the exponentiated Weibull distribution”, Metrika, vol. 62, pp. 17-22, 2005.
  • [12] A. K. Nanda, H. Singh, N. Misra, P. Paul, “Reliability properties of reversed residual lifetime”, Communications in Statistics-Theory and Methods, vol. 32, pp. 2031-2042, 2003.
  • [13] M. M. Nassar, F. H. Eissa, “On the exponentiated Weibull distribution”, Communications in Statistics-Theory and Methods, vol. 32, pp. 1317-1336, 2003.
  • [14] R. Tahmasbi, S. Rezaei, “A two-parameter lifetime distribution with decreasing failure rate”, Computational Statistics and Data Analysis, vol. 52, pp. 3889-3901, 2008.
  • [15] D. F. Andrews, A. M. Herzberg, “Data: A Collection of Problems from Many Fields for the Student and Research Worker”, Springer Series in Statistics, New York, 1985.
  • [16] L. Kamberi, T. Iljazi, S. Orhani, “Statistical Analysis on Information Technology Impact in Quality Learning of Mathematics (for Grades VI-IX)”, Journal of Natural Sciences and Mathematics of UT, vol. 6, no. 11-12, pp. 123-134, 2021.
  • [17] F. Merovci, I. Elbatal, “Weibull Rayleigh Distribution: Theory and Applications”, Appl. Math. Inf. Sci. Vol. 9, no. 4, pp. 2127-2137, 2015.
Year 2022, , 1084 - 1092, 31.12.2022
https://doi.org/10.16984/saufenbilder.1137262

Abstract

References

  • [1] G. T. Basheer, Z. Y. Algamal, “Reliability Estimation of Three Parameters Weibull Distribution based on Particle Swarm Optimization”, Pakistan Journal of Statistics and Operation Research, vol. 17, pp. 35-42, 2021.
  • [2] A. M. Abd Elfattah, A. S. Hassanand, D.M. Ziedan, “Efficiency of Maximum Likelihood Estimators under Different Censored Sampling Schemes for Rayleigh Distribution”, Interstat, 2006.
  • [3] R. D. Gupta, D. Kundu, “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrika Journal, vol. 43, pp. 117-130, 2001.
  • [4] E. K. AL-Hussaini, M. Ahsanullah, “Exponentiated Distributions”, Springer, vol. 5, 2015.
  • [5] G. S. Mudholkar, A. D. Hustson, “The exponentiated Weibull family: some properties and a flood data application”, Communications in Statistics-Theory and Methods, vol 25, pp. 3059-3083, 1996.
  • [6] K. Cooray, “Generalization of the Weibull distribution: the odd Weibull family”, Statistical Modelling, vol. 6, pp. 265-277, 2006.
  • [7] B. Marcelo, R. B. Silva , G. Cordeiro, “The Weibull - G Family of Probability Distributions”. Journal of Data Science, vol. 12, pp. 53-68, 2014.
  • [8] W. Barreto-Souza, A.H.S. Santos, G.M. Cordeiro, “The beta generalized exponential distribution”, Journal of Statistical Computation and Simulation, vol. 80, pp. 159-172, 2010.
  • [9] W. Barreto-Souza, A. L. Morais, G.M. Cordeiro, “The Weibull-geometric distribution”, Journal of Statistical Computation and Simulation, vol. 81, pp. 645-657, 2011.
  • [10] A. L. Morais, W. Barreto-Souza, “A compound class of Weibull and power series distributions”, Computational Statistics and Data Analysis, vol. 55, pp. 1410-1425, 2011.
  • [11] A. Choudhury, “A Simple derivation of moments of the exponentiated Weibull distribution”, Metrika, vol. 62, pp. 17-22, 2005.
  • [12] A. K. Nanda, H. Singh, N. Misra, P. Paul, “Reliability properties of reversed residual lifetime”, Communications in Statistics-Theory and Methods, vol. 32, pp. 2031-2042, 2003.
  • [13] M. M. Nassar, F. H. Eissa, “On the exponentiated Weibull distribution”, Communications in Statistics-Theory and Methods, vol. 32, pp. 1317-1336, 2003.
  • [14] R. Tahmasbi, S. Rezaei, “A two-parameter lifetime distribution with decreasing failure rate”, Computational Statistics and Data Analysis, vol. 52, pp. 3889-3901, 2008.
  • [15] D. F. Andrews, A. M. Herzberg, “Data: A Collection of Problems from Many Fields for the Student and Research Worker”, Springer Series in Statistics, New York, 1985.
  • [16] L. Kamberi, T. Iljazi, S. Orhani, “Statistical Analysis on Information Technology Impact in Quality Learning of Mathematics (for Grades VI-IX)”, Journal of Natural Sciences and Mathematics of UT, vol. 6, no. 11-12, pp. 123-134, 2021.
  • [17] F. Merovci, I. Elbatal, “Weibull Rayleigh Distribution: Theory and Applications”, Appl. Math. Inf. Sci. Vol. 9, no. 4, pp. 2127-2137, 2015.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Lazim Kamberi 0000-0001-6995-9189

Senad Orhani 0000-0003-3965-0791

Mirlinda Shaqiri 0000-0002-9330-8156

Sejhan Idrizi 0000-0003-1287-6571

Publication Date December 31, 2022
Submission Date June 29, 2022
Acceptance Date September 3, 2022
Published in Issue Year 2022

Cite

APA Kamberi, L., Orhani, S., Shaqiri, M., Idrizi, S. (2022). Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. Sakarya University Journal of Science, 26(6), 1084-1092. https://doi.org/10.16984/saufenbilder.1137262
AMA Kamberi L, Orhani S, Shaqiri M, Idrizi S. Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. SAUJS. December 2022;26(6):1084-1092. doi:10.16984/saufenbilder.1137262
Chicago Kamberi, Lazim, Senad Orhani, Mirlinda Shaqiri, and Sejhan Idrizi. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science 26, no. 6 (December 2022): 1084-92. https://doi.org/10.16984/saufenbilder.1137262.
EndNote Kamberi L, Orhani S, Shaqiri M, Idrizi S (December 1, 2022) Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. Sakarya University Journal of Science 26 6 1084–1092.
IEEE L. Kamberi, S. Orhani, M. Shaqiri, and S. Idrizi, “Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method”, SAUJS, vol. 26, no. 6, pp. 1084–1092, 2022, doi: 10.16984/saufenbilder.1137262.
ISNAD Kamberi, Lazim et al. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science 26/6 (December 2022), 1084-1092. https://doi.org/10.16984/saufenbilder.1137262.
JAMA Kamberi L, Orhani S, Shaqiri M, Idrizi S. Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. SAUJS. 2022;26:1084–1092.
MLA Kamberi, Lazim et al. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science, vol. 26, no. 6, 2022, pp. 1084-92, doi:10.16984/saufenbilder.1137262.
Vancouver Kamberi L, Orhani S, Shaqiri M, Idrizi S. Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. SAUJS. 2022;26(6):1084-92.

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