Main Article Content


This paper proposes a new three parameter Weibull distribution obtained using a new Transmutation technique namely New Transmuted Weibull distribution. A comprehensive account of some of the mathematical properties of new model are derived. Entropy estimation and parameter estimation is also carried out using different methods. Finally, it will be shown that the analytical results are applicable to model real data.


New Transmuted Weibull Distribution Reliability Entropy Moments Estimation.

Article Details

How to Cite
Malik, A. S., & Ahmad, S. (2022). A New Transmuted Weibull Distribution: Properties and Application. Pakistan Journal of Statistics and Operation Research, 18(2), 369-381.


  1. Alizadeh, M., Rasekhi, M., Yousuf, H.M., and Hamedani, G.G. (2017). The Transmuted Weibull-G family of Distributions. Hacettpe university Bulletin of Natural Sciences and Engineering Series B: Mthematics and Statistics, 47 (4), 1671-1689. DOI:
  2. Alqam, M., Bennett, R.M., and Zureick, A. H. (2002). Three-parameter vs. two-parameter Weibull distribution for pultruded composite material properties. Composite Structures, 58(4), 497-503. DOI:
  3. Bakouch, H., Jamal, F., Chesneau, C. and Nasir, A. (2017). A new transmuted family of distributions: Properties and estimation with applications. Available online at
  4. EL-Baset, A., Ahmad, A., and Ghazal, M.G.M. (2020). Exponentiated additive Weibull distribution. Reliability Engineering and System Safety, 193. DOI:
  5. Bourguignon, M., Silva, R. B. and Cordeiro, G. M. (2014). The Weibull-G family of Probability Distributions. Journal of Data Science, 12, 53-68. DOI:
  6. Hallinan, A. J. Jr. (1993). A review of the Weibull distribution. Journal of Quality Technology, 25, 85-93. DOI:
  7. Jan, U., Fatima, K., and Ahmad, S.P. (2017). Transmuted Exponentiated Inverse Weibull Distribution with Applications in Medical sciences. International Journal of Mathematics Trends and Technology, 50 ,160-167. DOI:
  8. Khalili, A., and Kromp, K. (1991). Statistical properties of Weibull estimators. Journal of Materials Science, 26, 6741-6752. DOI:
  9. Lee, E. T. and Wang, J. W. (2003). Statistical methods for sur¬vival data analysis. 3rd edition. John Wiley and Sons, New York, USA.
  10. Mahmood, F.H., Resen, A.K., and Khamees, A.B. (2020). Wind characteristic analysis based on Weibull distribution of Al-Salman site, Iraq. Energy Reports, 6(3), 79-87. DOI:
  11. Mathai, A.M., and Haubold, H. J. (2006). Pathway models, Tsalli entropy, superstatistics and a generalized measure of entropy. Physics A, 375,110-122. DOI:
  12. Mazucheli, J., Menezes, A. F. B., Fernandes, L. B., de Oliveira, R. P., and Ghitany, M. E. (2020). The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics, 47(6), 954-974, DOI: 10.1080/02664763.2019.1657813 DOI:
  13. Nassar, M., Alzaatreh, A., Mead, M., and Abo-Kasem, O. (2017). Alpha Power Weibull distribution: Properties and application. Communications in Statistics-Theory and Methods, 46(20), 10236-10252. DOI:
  14. Pal, M., Ali, M.M., and Woo, J. (2016).Exponentiated Weibull Distribuition, Statistica, 2.
  15. Renyi, A. (1961). On Measures of Information and Entropy. Proceedings of the Fourth Berkeley Symposium On Mathematics. Statistics And Probability, 547-561.
  16. Weibull, W. (1939). A statistical theory of the strength of material. Ing. Vetenskapa Acad. Handlingar, 151, 1–45.