Estimating Entropy of the Kumaraswamy Distribution with Contaminated Samples

Nass, Layla; Rasheed, Waleed

doi:10.25673/123741

Proceedings of International Conference on Applied Innovation in IT · 2026/03/31 · Vol. 14 · Issue 1 · pp. 1367–1376

Estimating Entropy of the Kumaraswamy Distribution with Contaminated Samples

Layla M. Nass, Waleed Abdullah Araheemah and Husam Abdulrazzak Rasheed

📄 Download PDF DOI: 10.25673/123741

Abstract

Kumaraswamy distribution (KD) is essential for many applications and experiments in renewable energy and geophysics. The distribution has many applied functions that depend on the accuracy of the distribution parameter estimates. Several simulation experiments were carried out based on the change in each of (polluted ratios (ϖ_i), sample sizes (n_i), and proposal parameter values (α_i ,β_i) and estimation methods with the (Maximum Likelihood Estimation Method (MLE), Moment Method (MOM) and Mixed Method (MM))and studying the effect of the change in each of them on the distribution parameter estimates and the entropy function of the distribution function. The results of the simulation experiments were compared through the mean square error, and the results showed the effect of the function estimator on the change in each of the (ϖ_i, n_i, α_i ,β_i) and the estimation method. Simulation experiments can be carried out on other distributions (Weibull, beta, Normal), and methods of estimating ((Bayesian, Shrinkage)) can be carried out on the (KD).

Keywords

Kumaraswamy Distribution Maximum Likelihood Estimation Method Moment Method Mixed Method Entropy Function.

References

M. Mohie Eldin, “Estimation of Parameters of the Kumaraswamy Distribution Based on General Progressive Type II Censoring,” American Journal of Theoretical and Applied Statistics, vol. 3, no. 6, 2014, p. 217, doi: 10.11648/j.ajtas.20140306.17.
S.-J. Chen and C.-L. Hwang, “Fuzzy Multiple Attribute Decision Making Methods,” Fuzzy Multiple Attribute Decision Making, 1992, pp. 289-486, doi: 10.1007/978-3-642-46768-4_5.
H. G. Simbolon, I. Fithriani, and S. Nurrohmah, “Estimation of shape β parameter in Kumaraswamy distribution using Maximum Likelihood and Bayes method,” AIP Conference Proceedings, vol. 1862, 2017, p. 030160, doi: 10.1063/1.4991264.
George and S. Thobias, “Marshall-Olkin Kumaraswamy Distribution,” International Mathematical Forum, vol. 12, no. 2, 2017, pp. 47-69, [Online]. Available: https://doi.org/10.12988/imf.2017.611151.
A. S. Hassan and S. A. Atia, “Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling with unequal samples,” Scientific Reports, vol. 14, no. 1, Oct. 2024, doi: 10.1038/s41598-024-74468-4.
E.-S. El-Sherpieny and M. Ahmed, “On the Kumaraswamy Kumaraswamy distribution,” International Journal of Basic and Applied Sciences, vol. 3, no. 4, Sep. 2014, doi: 10.14419/ijbas.v3i4.3182.
B. E. Mohammed, “Statistical Properties of Kumaraswamy-Generalized Exponentiated Exponential Distribution,” International Journal of Computer Applications, vol. 94, no. 4, May 2014, pp. 1-8, doi: 10.5120/16328-5602.
M. S. Khan, R. King, and I. L. Hudson, “Transmuted Kumaraswamy Distribution,” Statistics in Transition New Series, vol. 17, no. 2, Jun. 2016, pp. 183-210, doi: 10.21307/stattrans-2016-013.
L. M. Nassir, H. A. Rasheed, and A. A. R. Rasheed, “The effect of polluted samples on Bayesian Estimators of Burr type –XII distribution,” Periodicals of Engineering and Natural Sciences (PEN), vol. 10, no. 2, Apr. 2022, p. 337, doi: 10.21533/pen.v10i2.2862.
A. J. Lemonte, W. Barreto-Souza, and G. M. Cordeiro, “The exponentiated Kumaraswamy distribution and its log-transform,” Brazilian Journal of Probability and Statistics, vol. 27, no. 1, Feb. 2013, doi: 10.1214/11-bjps149.
R. I. Kadhim, et al., “AI-enhanced Cybersecurity in Fluid Dynamics Simulation Software,” 2024 8th International Symposium on Innovative Approaches in Smart Technologies (ISAS), pp. 1-8, Dec. 2024, doi: 10.1109/isas64331.2024.10845531.
A. A. Hadi, et al., “Machine Learning Techniques for Turbulence Analysis and Simulation,” 2024 8th International Symposium on Innovative Approaches in Smart Technologies (ISAS), pp. 1-7, Dec. 2024, doi: 10.1109/isas64331.2024.10845730.
M. Abdualwhab, J. Gareed, A. J. Al-Shimary, H. B. Furaijl, S. R. Ahmed, and S. Algburi, “Leveraging IoT Data for Real-Time Business Decision-Making,” 2024 8th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT), pp. 1-8, Nov. 2024, doi: 10.1109/ismsit63511.2024.10757297.