SavedAdd your journal

Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :B-Teorik Bilimler / 2018 / Cilt: 6 - Sayı: 1

THE DOUBLY-TRUNCATED EXPONENTIATED INVERSE WEIBULL DISTRIBUTION

Demet AYDIN
Pages
55–74
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, a real dataexample is given to show the applicability of the proposed distribution.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we introduce the five-parameter doubly-truncated exponentiated inverse Weibull distribution, where thetruncation points are known, and consider its basic properties.
📊
Key Findings & Data:A Monte-Carlo simulationstudy is designed and conducted to evaluate the performances of obtained estimators of parameters.
💡
Conclusion & Impact:Finally, a real dataexample is given to show the applicability of the proposed distribution.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, we introduce the five-parameter doubly-truncated exponentiated inverse Weibull distribution, where thetruncation points are known, and consider its basic properties. Formulas for moment generating function, characteristicfunction, mean, variance and kurtosis of the distribution are derived. Estimates of parameters are obtained using traditionalestimation methods; maximum likelihood, least squares and weighted least squares. Furthermore, in order to give a lowerbound for the standard errors of estimates of parameters, a Fisher information matrix is provided. A Monte-Carlo simulationstudy is designed and conducted to evaluate the performances of obtained estimators of parameters. Finally, a real dataexample is given to show the applicability of the proposed distribution.

🔖

Cite This Article

AYDIN, D. (2022). THE DOUBLY-TRUNCATED EXPONENTIATED INVERSE WEIBULL DISTRIBUTION. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :B-Teorik Bilimler, Cilt: 6 - Sayı: 1, 55–74. https://ajindex.com/articles/438545

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Afify AZ, Nofal ZM, Butt NS. Transmuted complementary Weibull geometric distribution. Pakistan Journal of Statistics and Operation Research 2014; 10(4): 435–454
  2. Ahmad AA. Moments of order statistics from doubly truncated continuous distribution. Statistics 2001; 35: 479–494
  3. Ali MM, Pal M, Woo JS. Some exponentiated distributions. Communications for Statistical Applications and Methods 2007; 14(1): 93–109
  4. Al-Matrafi BN, Jawa TM. Recurrence relations for single moments of generalized order statistics from doubly truncated continuous distributions. Journal of King Abdulaziz University: Science 2008; 20(2): 79–89
  5. Calabria R, Pulcini G. Confidence limits for reliability and tolerance limits in the inverse Weibull distribution. Reliability Engineering & System Safety 1989; 24(1): 77–85
  6. Cohen AC, Whitten BJ. Parameter estimation in reliability and life span models. New York and Basel: Marcel Dekker Inc., 1988
  7. Coffey CS, Muller KE. Properties of doubly-truncated gamma variables. Communications in Statistics-Theory and Methods 2000; 29(4): 851–857. [8] de Gusmão FR, Ortega EM, Cordeiro, GM. The generalized inverse Weibull distribution. Statistical Papers 2011; 52(3): 591–619
  8. Foss S, Korshunov D, Zachary S. An introduction to heavy-tailed and subexponential distributions. New York: Springer, 2011
  9. Gupta RC, Gupta PL, Gupta RD. Modeling failure time data by Lehman alternatives. Communications in Statistics, Theory and Methods 1998; 27: 887–904
  10. Gupta RD, Kundu D. Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biometrical Journal 2001; 43: 117–130
  11. Jiang R, Murthy DNP, Ji P. Models involving two inverse Weibull distributions. Reliability Engineering & System Safety 2001; 73(1): 73–81
  12. Johnson NL, Kotz S, Balakrishnan N. Continuous Univariate Distribution, Vol. 2, 2nd edition, New York: Wiley, 1995
  13. Joshi PC. A note on the moments of order statistics from doubly truncated exponential distribution. Annals of the Institute of Statistical Mathematics 1979; 31: 321–324
  14. Keller AZ, Kamath ARR, Perera UD. Reliability analysis of CNC machine tools. Reliability Engineering 1982; 3: 449–473
  15. Kantar YM, Usta I. Analysis of the upper-truncated Weibull distribution for wind speed. Energy Conversion and Management 2015; 96: 81–88
  16. Khan MS, Pasha GR, Pasha AH. Theoretical analysis of inverse Weibull distribution.WSEAS Transactions on Mathematics 2008; 7(2): 30–38. [18