A new inverse Weibull distribution with properties, estimation, simulation, and applications

Authors

  • Muhammad Osama Department of Statistics, University of Peshawar
  • Sayed Alamgir Shah Department of Statistics, University of Peshawar
  • Syed Muhammad Zeeshan Department of Statistics, University of Peshawar
  • Muhammad Haseeb Ullah Department of Statistics, University of Peshawar

DOI:

https://doi.org/10.64497/jssci.149

Abstract

This study offers a new probability distribution to improve the modeling of lifetime data. The main statistical properties of the distribution, including its quantile function, moments, and moment generating function, are derived. The model parameters are estimated using the method of maximum likelihood (MLE), and a simulation study is conducted to evaluate the performance and accuracy of the MLEs under different sample sizes and parameter settings. To demonstrate its practical usefulness, the proposed distribution is applied to three real datasets and compared with several existing competing distributions. The goodness-of-fit tests show that the proposed distribution fits the data better than the competing models.

Downloads

Download data is not yet available.

References

[1] Khan, M. S., Pasha, G. R., & Pasha, A. H. (2008). Theoretical analysis of inverse Weibull distribution. WSEAS Transactions on Mathematics, 7(2), 30-38.

[2] De Gusmao, F. R., Ortega, E. M., & Cordeiro, G. M. (2011). The generalized inverse Weibull distribution. Statistical Papers, 52(3), 591-619. DOI: https://doi.org/10.1007/s00362-009-0271-3

[3] Jazi, M. A., Lai, C. D., & Alamatsaz, M. H. (2010). A discrete inverse Weibull distribution and estimation of its parameters. Statistical methodology, 7(2), 121-132. DOI: https://doi.org/10.1016/j.stamet.2009.11.001

[4] Akgül, F. G., Şenoğlu, B., & Arslan, T. (2016). An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234-240. DOI: https://doi.org/10.1016/j.enconman.2016.02.026

[5] Khan, M. S., & King, R. (2012). Modified inverse Weibull distribution. Journal of statistics applications & Probability, 1(2), 115. DOI: https://doi.org/10.12785/jsap/010204

[6] Hanook, S., Shahbaz, M. Q., Mohsin, M., & Golam Kibria, B. M. (2013). A note on beta inverse-Weibull distribution. Communications in Statistics-Theory and Methods, 42(2), 320-335. DOI: https://doi.org/10.1080/03610926.2011.581788

[7] Shahbaz, M. Q., Shahbaz, S., & Butt, N. S. (2012). The Kumaraswamy Inverse Weibull Distribution. Pakistan journal of statistics and operation research, 479-489. DOI: https://doi.org/10.18187/pjsor.v8i3.520

[8] Okasha, H. M., El-Baz, A. H., Tarabia, A. M. K., & Basheer, A. M. (2017). Extended inverse Weibull distribution with reliability application. Journal of the Egyptian Mathematical Society, 25(3), 343-349. DOI: https://doi.org/10.1016/j.joems.2017.02.006

[9] Basheer, A. M. (2019). Alpha power inverse Weibull distribution with reliability application. Journal of Taibah University for Science, 13(1), 423-432. DOI: https://doi.org/10.1080/16583655.2019.1588488

[10] Elbatal, I., & Muhammed, H. Z. (2014). Exponentiated generalized inverse Weibull distribution. Applied Mathematical Sciences, 8(81), 3997-4012. DOI: https://doi.org/10.12988/ams.2014.44267

[11] Pararai, M., Warahena-Liyanage, G., & Oluyede, B. O. (2014). A new class of generalized inverse Weibull distribution with applications. Journal of Applied Mathematics and Bioinformatics, 4(2), 17.

[12] Muhammed, H. Z. (2016). Bivariate inverse Weibull distribution. Journal of Statistical Computation and Simulation, 86(12), 2335-2345. DOI: https://doi.org/10.1080/00949655.2015.1110585

[13] Khalaf, A. A., Noori, N., & Khaleel, M. (2024). A new expansion of the Inverse Weibull Distribution: Properties with Applications. Iraqi Statisticians journal, 52-62. DOI: https://doi.org/10.62933/sdkgcy19

[14] Afify, A. Z., Ahmed, S., & Nassar, M. (2021). A new inverse Weibull distribution: properties, classical and Bayesian estimation with applications. Kuwait Journal of Science, 48(3). DOI: https://doi.org/10.48129/kjs.v48i3.9896

[15] Khan, M. S., & King, R. (2012). Transmuted generalized inverse Weibull distribution. Journal of Applied Statistical Science, 20(3), 213.

[16] Mahmoud, M. A. W., Sultan, K. S., & Amer, S. M. (2003). Order statistics from inverse Weibull distribution and associated inference. Computational statistics & data analysis, 42(1-2), 149-163. DOI: https://doi.org/10.1016/S0167-9473(02)00151-2

[17] Kumar, K., & Kumar, I. (2019). Estimation in inverse Weibull distribution based on randomly censored data. Statistica, 79(1), 47-74.

[18] Pakungwati, R. M., Widyaningsih, Y., & Lestari, D. (2018, November). Marshall-Olkin extended inverse Weibull distribution and its application. In Journal of physics: conference series (Vol. 1108, No. 1, p. 012114). IOP Publishing. DOI: https://doi.org/10.1088/1742-6596/1108/1/012114

[19] Abbas, S., Taqi, S. A., Mustafa, F., Murtaza, M., & Shahbaz, M. Q. (2017). Topp-Leone inverse Weibull distribution: theory and application. European Journal of Pure and Applied Mathematics, 10(5), 1005-1022.

[20] Sultan, K. S., Ismail, M. A., & Al-Moisheer, A. S. (2007). Mixture of two inverse Weibull distributions: Properties and estimation. Computational Statistics & Data Analysis, 51(11), 5377-5387. DOI: https://doi.org/10.1016/j.csda.2006.09.016

[21] Tashkandy, Y. A., Elshenawy, A., Tekle, G. M., Bakr, M. E., & Balogun, O. S. (2024). A novel distributional approach based on the trigonometric function with medical data sets. Alexandria Engineering Journal, 96, 303-322. DOI: https://doi.org/10.1016/j.aej.2024.03.076

[22] Nichols, M. D., & Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles. Quality and reliability engineering international, 22(2), 141-151. DOI: https://doi.org/10.1002/qre.691

[23] Mahmoud, M. R., & Mandouh, R. M. (2013). On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9(10), 5553-5561.

[24] Tomer, S. K., & Panwar, M. S. (2020). A review on Inverse Maxwell distribution with its statistical properties and applications. Journal of Statistical Theory and Practice, 14(3), 33. DOI: https://doi.org/10.1007/s42519-020-00100-z

Downloads

Published

2025-12-04

How to Cite

Muhammad Osama, Sayed Alamgir Shah, Syed Muhammad Zeeshan, & Muhammad Haseeb Ullah. (2025). A new inverse Weibull distribution with properties, estimation, simulation, and applications. Journal of Statistical Sciences and Computational Intelligence, 1(4), 351–370. https://doi.org/10.64497/jssci.149

Issue

Vol. 1 No. 4 (2025): Volume 1, Issue 4 (October – December 2025)

Section

Articles

License

Copyright (c) 2025 Muhammad Osama, Sayed Alamgir Shah, Syed Muhammad Zeeshan, Muhammad Haseeb Ullah

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Views
  • Abstract 332
  • PDF 121