Estimate the interval of the fuzzy parameters of the inverse Weibull distribution

Document Type : Research Paper


Department of Statistics, University of Karbala, Karbala, Iraq


In this article, two estimation methods are used to estimate the interval of the parameters for the inverse Weibull distribution in the case of fuzzy data. These two methods are based on, the maximum likelihood method and the relative maximum likelihood method. In addition, we compare the Maximum likelihood intervals with relative maximum likelihood intervals for both real and fuzzy data. The results of the comparison showed that the fuzziness interval estimation is better than the real one. Examples of applications are given.


[1] S. Alkarni, A.Z. Afify, I. Elbatal, and M. Elgarhy, The extended inverse weibull distribution: properties and applications, Complexity 2020 (2020).
[2] G. Chen and T.T. Pham, Introduction to fuzzy sets, fuzzy logic, and fuzzy control systems, CRC press, 2000.
[3] Antoni Drapella, The complementary weibull distribution: unknown or just forgotten?, Qual. Reliab. Engin. Int. 9 (1993), no. 4, 383–385.
[4] R.V. Hogg and A.T. Craig, Introduction to mathematical statistics.(5”” edition), Englewood Hills, New Jersey, 1995.
[5] M.S. Khan, G.R. Pasha, and A.H. Pasha, Theoretical analysis of inverse weibull distribution, WSEAS Trans. Math. 7 (2008), no. 2, 30–38.
[6] K.H. Lee, First course on fuzzy theory and applications, vol. 27, Springer Science & Business Media, 2004.
[7] R.M. Mweleli, L.A. Orawo, C.L. Tamba, and J.O. Okenye, Interval estimation in a two parameter weibull distribution based on type-2 censored data, Open J. Statist. 10 (2020), no. 06, 1039.
[8] E. N´ajera and A. Bol´─▒var-Cim´e, Comparison of some interval estimation methods for the parameters of the gamma distribution, Commun. Statist. Simul. Comput. (2021), 1–17.
[9] A. Pak, Inference for the shape parameter of lognormal distribution in presence of fuzzy data, Pakistan J. Statist. Oper. Res. (2016), 89–99.
[10] A. Pak, G.A. Parham, and M. Saraj, Reliability estimation in rayleigh distribution based on fuzzy lifetime data, Int. J. Syst. Assur. Engin. Manag. 5 (2014), no. 4, 487–494.
[11] P.L. Ramos, D. Nascimento, and F. Louzada, The long term fr\’echet distribution: Estimation, properties and its application, arXiv preprint arXiv:1709.07593 (2017).
[12] T. Tao, An introduction to measure theory, vol. 126, American Mathematical Society Providence, 2011.
[13] H. Torabi and S.M. Mirhosseini, The most powerful tests for fuzzy hypotheses testing with vague data, Appl. Math. Sci. 3 (2009), no. 33, 1619–1633.
[14] H.-C. Wu, Fuzzy reliability estimation using bayesian approach, Comput. Ind. Engin. 46 (2004), no. 3, 467–493.
[15] L.A. Zadeh, Zadeh, fuzzy sets, Inf. Control 8 (1965), 338–353.
[16] , Fuzzy algorithms, Inf. Control 12 (1968).
[17] H.-J. Zimmermann, Fuzzy set theory—and its applications, Kluwer, Nijhoff Publishing, Boston, 1985.
Volume 14, Issue 1
January 2023
Pages 2481-2491
  • Receive Date: 16 September 2022
  • Revise Date: 07 November 2022
  • Accept Date: 01 January 2023