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

Year 2022, Volume 26, Issue 6, 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, Volume 26, Issue 6, 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.

Details

Primary Language English
Subjects Mathematics
Journal Section Research Articles
Authors

Lazim KAMBERİ>
University of Tetova
0000-0001-6995-9189
Macedonia


Senad ORHANİ> (Primary Author)
University of Prishtina "Hasan Prishtina"
0000-0003-3965-0791
Kosovo


Mirlinda SHAQİRİ>
University of Tetova
0000-0002-9330-8156
Macedonia


Sejhan IDRİZİ>
University of Tetova
0000-0003-1287-6571
Macedonia

Publication Date December 31, 2022
Submission Date June 29, 2022
Acceptance Date September 3, 2022
Published in Issue Year 2022, Volume 26, Issue 6

Cite

Bibtex @research article { saufenbilder1137262, journal = {Sakarya University Journal of Science}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2022}, volume = {26}, number = {6}, pages = {1084 - 1092}, doi = {10.16984/saufenbilder.1137262}, title = {Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method}, key = {cite}, author = {Kamberi, Lazim and Orhani, Senad and Shaqiri, Mirlinda and Idrizi, Sejhan} }
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 . DOI: 10.16984/saufenbilder.1137262
MLA Kamberi, L. , Orhani, S. , Shaqiri, M. , Idrizi, S. "Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method" . Sakarya University Journal of Science 26 (2022 ): 1084-1092 <https://dergipark.org.tr/en/pub/saufenbilder/issue/74051/1137262>
Chicago Kamberi, L. , Orhani, S. , Shaqiri, M. , Idrizi, S. "Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method". Sakarya University Journal of Science 26 (2022 ): 1084-1092
RIS TY - JOUR T1 - Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method AU - LazimKamberi, SenadOrhani, MirlindaShaqiri, SejhanIdrizi Y1 - 2022 PY - 2022 N1 - doi: 10.16984/saufenbilder.1137262 DO - 10.16984/saufenbilder.1137262 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1084 EP - 1092 VL - 26 IS - 6 SN - -2147-835X M3 - doi: 10.16984/saufenbilder.1137262 UR - https://doi.org/10.16984/saufenbilder.1137262 Y2 - 2022 ER -
EndNote %0 Sakarya University Journal of Science Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method %A Lazim Kamberi , Senad Orhani , Mirlinda Shaqiri , Sejhan Idrizi %T Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method %D 2022 %J Sakarya University Journal of Science %P -2147-835X %V 26 %N 6 %R doi: 10.16984/saufenbilder.1137262 %U 10.16984/saufenbilder.1137262
ISNAD Kamberi, Lazim , Orhani, Senad , Shaqiri, Mirlinda , Idrizi, Sejhan . "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
AMA 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): 1084-1092.
Vancouver Kamberi L. , Orhani S. , Shaqiri M. , Idrizi S. Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method. Sakarya University Journal of Science. 2022; 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", Sakarya University Journal of Science, vol. 26, no. 6, pp. 1084-1092, Dec. 2022, doi:10.16984/saufenbilder.1137262

Sakarya University Journal of Science (SAUJS)