Evaluation of Relative Loss in Odd Generalised Exponential Burr Type X and Truncated Odd Generalised Exponential Burr Type X Distributions

Authors

  • Murtadha M.Jasim Department of Mathematics, Collage of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq. Author
  • Moudher Kh. Abdal-hammed Department of public Administration, Collage of Administration and Economics, Tikrit University, Tikrit, Iraq Author
  • Mizal Alobaidy Department of Mathematics, Collage of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq. Author
  • Alaa A. Khalaf Ministry of Education, Diyala Education Directorate, Diyala, Iraq. Author https://orcid.org/0009-0000-5496-3089

DOI:

https://doi.org/10.62933/0vvgte14

Keywords:

OGE Burr Type X, Truncated Burr Type X, Entropies, Relative loss, Burr Type X distribution

Abstract

This paper presents derivation entropy measures for two types of distributions: the Odd Generalised Exponential Burr type X distribution (OGEBX) and the truncated Odd Generalised Exponential Burr type X distribution (TOGEBX). The relative loss was achieved by testing a set of different parameter values. In the context of certain distributions, the optimistic results of this study can be applied. Based on the lowest value of each distribution, a numerical comparison was made between the entropy measures to select the optimal one. The relative loss was then determined using all six measures. When the OGE Burr Type X distribution is not used on [0, ∞], but the truncated OGE Burr Type X distribution on [0, t] is used.

References

[1] Dey, S., Maiti, S. S., & Ahmad, M. (2016). Pak. J. Statist. 2016 Vol. 32 (2), 97-108 COMPARISON OF DIFFERENT ENTROPY MEASURES. Pak. J. Statist, 32(2), 97-108.‏

[2] Basit, A., Riaz, A., Iqbal, Z., & Ahmad, M. (2017). On comparison of entropy measures for weighted and truncated weighted exponential distributions. Advances and Applications in Statistics, 50(6), 477-495.‏

[3] Mir, K. A., Ahmed, A., & Reshi, J. A. (2013). On size-biased exponential distribution. Journal of Modern Mathematics and Statistics, 7(2), 21-25.‏

[4] AWAD, A. M., & ALAWNEH, A. J. (1987). Application of entropy to a life-time model. IMA Journal of Mathematical Control and Information, 4(2), 143-148.‏

[5] Ijaz, M., AL-Aziz, S. N., Asim, S. M., Dar, J. G., & Abd El-Bagoury, A. A. H. (2021). Comparison of different entropy measures using the relative loss approach for the lomax distribution. Information Sciences Letters, 10(3), 18.‏

[6] Al-Babtain, A. A., Elbatal, I., Chesneau, C., & Elgarhy, M. (2021). Estimation of different types of entropies for the Kumaraswamy distribution. PLoS One, 16(3), e0249027.

‏[7] Teixeira, A., Matos, A., Souto, A., & Antunes, L. (2011). Entropy measures vs. Kolmogorov complexity. Entropy, 13(3), 595-611.‏

[8] Baez, J. C., Fritz, T., & Leinster, T. (2011). A characterization of entropy in terms of information loss. Entropy, 13(11), 1945-1957.

[9] Zaman, Q., Bilal, M., Ijaz, M., & Ullah, N. (2022). Performance of Various Entropy Measures: Applications to Pareto and Truncated Pareto Distributions. The Lighthouse Journal of Computational & Numerical Sciences, 1(01), 33-58.‏

[10] Ahsan ul Haq, M., & Aslam, M. (2023). Comparison of Entropy Measures for Gompertz and Truncated Gompertz Distribution. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 93(1), 113-120.‏

[11] Ebrahimi, N., Pflughoeft, K., & Soofi, E. S. (1994). Two measures of sample entropy. Statistics & Probability Letters, 20(3), 225-234.‏

[12] Abo-Eleneen, Z. A. (2011). The entropy of progressively censored samples. Entropy, 13(2), 437-449.‏

[131] Cho, Y., Sun, H., & Lee, K. (2014). An estimation of the entropy for a Rayleigh distribution based on doubly-generalized Type-II hybrid censored samples. Entropy, 16(7), 3655-3669.‏

[14] Hassan, A. S., & Zaky, A. N. (2019). Estimation of entropy for inverse Weibull distribution under multiple censored data. Journal of Taibah University for Science, 13(1), 331-337.

‏[15] Bantan, R. A., Elgarhy, M., Chesneau, C., & Jamal, F. (2020). Estimation of entropy for inverse Lomax distribution under multiple censored data. Entropy, 22(6), 601.‏

[16] Kayal, S., & Kumar, S. (2013). Estimation of the Shannon’s entropy of several shifted exponential populations. Statistics & Probability Letters, 83(4), 1127-1135.‏

[17] Cho, Y., Sun, H., & Lee, K. (2015). Estimating the entropy of a Weibull distribution under generalized progressive hybrid censoring. Entropy, 17(1), 102-122.‏

[18] Noorizadeh, S., & Shakerzadeh, E. (2010). Shannon entropy as a new measure of aromaticity, Shannon aromaticity. Physical Chemistry Chemical Physics, 12(18), 4742-4749.‏

[191] Khalaf, A. A., & khaleel, M. A. (2022, November). [0, 1] Truncated exponentiated exponential gompertz distribution: Properties and applications. In AIP Conference Proceedings (Vol. 2394, No. 1, p. 070035). AIP Publishing LLC.‏

[20] Khalaf, A., & Khaleel, M. A. (2020). Truncated exponential marshall-olkin-gompertz distribution properties and applications. Tikrit Journal of Administration and Economics Sciences, 16, 483-497.‏

[21] Al-Habib, K. H., Abdal-hammed, M. K., Salih, A. M., & Hemeda, S. E. (2024). Statistical Properties and Parameters Estimation for a New Truncated Lomax Exponential-G Family. Samarra Journal of Pure and Applied Science, 6(4), 255-270.‏

[22] Khalaf, A., Yusur, K., & Khaleel, M. (2023). [0, 1] Truncated Exponentiated Exponential Inverse Weibull Distribution with Applications of Carbon Fiber and COVID-19 Data. Journal of Al-Rafidain University College For Sciences (Print ISSN: 1681-6870, Online ISSN: 2790-2293), (1), 387-399.‏

[23] Al-Habib, K. H., Salih, A. M., Abdal-Hammed, M. K., Khaleel, M. A., & Algamal, Z. Y. (2025, March). Estimating the parameters of [0, 1] Truncated Nadarajah–Haghighi inverse weibull distribution. In AIP Conference Proceedings (Vol. 3264, No. 1, p. 050051). AIP Publishing LLC.‏

[24] Khalaf, A. A., Ibrahim, M. Q., & Noori, N. A. (2024). [0, 1] Truncated Exponentiated Exponential Burr type X Distributionwith Applications. Iraqi Journal of Science, 4428-4440.

‏[25] Khaleel, M. A., Abdulwahab, A. M., Gaftan, A. M., & Abdal-hammed, M. K. (2022). A new [0, 1] truncated inverse Weibull rayleigh distribution properties with application to COVID-19. International Journal of Nonlinear Analysis and Applications, 13(1), 2933-2946.‏

[26] Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423.

[27] Gemeay, A. M., Alsadat, N., Chesneau, C., & Elgarhy, M. (2024). Power unit inverse Lindley distribution with different measures of uncertainty, estimation and applications. AIMS Mathematics, 9(8), 20976-21024.‏

[28] Rényi A (1961) On measures of entropy and information. In: Proceedings of the fourth Berkeley symposium on mathematical statistics and probability, pp 547–561.

[29] Khalaf, A. A., & Khaleel, M. A. (2025). Estimation Methods: Inference Classical and Bayesian of Extended Inverse Exponential Distribution. Iraqi Statisticians journal, 29-42.‏

[30] Bashiru, S. O., Isa, A. M., Khalaf, A. A., Khaleel, M. A., Arum, K. C., & Anioke, C. L. (2025). A Hybrid Cosine Inverse Lomax-G Family of Distributions with Applications in Medical and Engineering Data. Nigerian Journal of Technological Development, 22(1), 261-278.‏

[31] Khalaf, A. A., & Khaleel, M. A. (2025, March). The Odd Burr XII Exponential distribution: Properties and applications. In AIP Conference Proceedings (Vol. 3264, No. 1, p. 050039). AIP Publishing LLC.‏

[32] Isa, A. M., Khalaf, A. A., & Bashiru, S. O. (2024). Some Properties of the Cosine Lomax Distribution with Applications.‏

[33] Habib, K. H., Salih, A. M., Khaleel, M. A., & Abdal-hammed, M. K. (2023). OJCA Rayleigh distribution, Statistical Properties with Application. Tikrit Journal of Administration and Economics Sciences, 19.‏

[34] Noori, N. A., Khalaf, A. A., & Khaleel, M. A. (2023). A New Generalized Family of Odd Lomax-G Distributions: Properties and Applications. Advances in the Theory of Nonlinear Analysis and its Applications, 7(4), 01-16.‏

[35] Bashiru, S. O., Khalaf, A. A., Isa, A. M., & Kaigama, A. (2024). ON MODELING OF BIOMEDICAL DATA WITH EXPONENTIATED GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION. Reliability: Theory & Applications, 19(3 (79)), 460-475.

‏[36] Murtadha M. J., Moudher Kh. A., Mizal A., (2025). Using Simulation to Estimate Parameters for a Novel Extension Rayleigh Distribution, Properties and Failure Rate Data Application, 28(7), 596-618.

[37] Khalaf, A. A., Khaleel, M. A., Jawa, T. M., Sayed-Ahmed, N., & Tolba, A. H. (2025). A Novel Extension of the Inverse Rayleigh Distribution: Theory, Simulation, and Real-World Application. Appl. Math, 19(2), 467-488.‏

[38] Isa, A. M., Bashiru, S. O., & Kaigama, A. (2024). Topp-Leone Exponentiated Burr XII Distribution: Theory and Application to Real-Life Data Sets. Iraqi Statisticians Journal, 1(1), 63-72.‏

[39] Bashiru, S. O., Khalaf, A. A., & Isa, A. M. (2024). TOPP-LEONE EXPONENTIATED GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION: PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications, 19(3 (79)), 59-77.‏

[40] Khalaf, A. A. (2024). The New Strange Generalized Rayleigh Family: Characteristics and Applications to COVID-19 Data. Iraqi Journal For Computer Science and Mathematics, 5(3), 32.‏

[41] Noori, N. A., Khalaf, A. A., & Khaleel, M. A. (2024). A new expansion of the Inverse Weibull Distribution: Properties with Applications. Iraqi Statistians Journal, 1(1), 52-62.‏

[42] Havrda J, Charvát F (1967) Quantification method of classification processes. Concept of structural a-entropy. Kybernetika 3:30–35.

[43] Alahmadi, A. A., ZeinEldin, R. A., Albalawi, O., Badr, M. M., Abdelfadel, T. A. A., & Shawki, A. W. (2025). Modified Kies power Lomax model with applications in different sciences. Journal of Radiation Research and Applied Sciences, 18(1), 101239.‏

[44] Arimoto S (1971) Information-theoretical considerations on estimation problems. Inf Control 19:181–194.

[45] Sharma BD, Mittal DP (1977) New non-additive measures of relative information. J Comb Inf Syst Sci 2:122–132.

[46] Mondaini, R. P., & de Albuquerque Neto, S. C. (2021). Alternative Entropy Measures and Generalized Khinchin–Shannon Inequalities. Entropy, 23(12), 1618.‏

[47] Tsallis C (1988) Possible generalization of Boltzmann–Gibbs statistics.J Stat Phys 52:479–487.

[48] Suleiman, A. A., Daud, H., Ishaq, A. I., Kayid, M., Sokkalingam, R., Hamed, Y., ... & Elgarhy, M. (2024). A new Weibull distribution for modeling complex biomedical data. Journal of Radiation Research and Applied Sciences, 17(4), 101190.‏

[49] Jasim, M. M., Abdal-Hammed, M. K., & Alobaidi, M. (2025, March). The Odd Generalized Exponential Burr type X distribution: Theorems and applications. In AIP Conference Proceedings (Vol. 3264, No. 1). AIP Publishing.‏

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Published

2025-07-21

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Vol 2, no. 2, 2025

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Copyright (c) 2025 Murtadha M.Jasim, Moudher Kh. Abdal-hammed, Mizal Alobaidy, Alaa A. Khalaf (Author)

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How to Cite

Evaluation of Relative Loss in Odd Generalised Exponential Burr Type X and Truncated Odd Generalised Exponential Burr Type X Distributions. (2025). Iraqi Statisticians Journal, 2(2), 64-78. https://doi.org/10.62933/0vvgte14