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

Yıl 2022, Cilt: 26 Sayı: 6, 1084 - 1092, 31.12.2022
https://doi.org/10.16984/saufenbilder.1137262

Öz

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.

Kaynakça

  • [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.
Yıl 2022, Cilt: 26 Sayı: 6, 1084 - 1092, 31.12.2022
https://doi.org/10.16984/saufenbilder.1137262

Öz

Kaynakça

  • [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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Lazim Kamberi 0000-0001-6995-9189

Senad Orhani 0000-0003-3965-0791

Mirlinda Shaqiri 0000-0002-9330-8156

Sejhan Idrizi 0000-0003-1287-6571

Yayımlanma Tarihi 31 Aralık 2022
Gönderilme Tarihi 29 Haziran 2022
Kabul Tarihi 3 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 26 Sayı: 6

Kaynak Göster

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. Aralık 2022;26(6):1084-1092. doi:10.16984/saufenbilder.1137262
Chicago Kamberi, Lazim, Senad Orhani, Mirlinda Shaqiri, ve Sejhan Idrizi. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science 26, sy. 6 (Aralık 2022): 1084-92. https://doi.org/10.16984/saufenbilder.1137262.
EndNote Kamberi L, Orhani S, Shaqiri M, Idrizi S (01 Aralık 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, ve S. Idrizi, “Comparison of Three-Parameter Weibull Distribution Parameter Estimators with the Maximum Likelihood Method”, SAUJS, c. 26, sy. 6, ss. 1084–1092, 2022, doi: 10.16984/saufenbilder.1137262.
ISNAD Kamberi, Lazim vd. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science 26/6 (Aralık 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 vd. “Comparison of Three-Parameter Weibull Distribution Parameter Estimators With the Maximum Likelihood Method”. Sakarya University Journal of Science, c. 26, sy. 6, 2022, ss. 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.