A Note on Transmuted Exponentiated Inverse Exponential Distribution and Application to Breast Cancer Data
Keywords:
TEIE, QRTM, Reliability Function, Hazard Rate Function, Maximum Likelihood
Abstract
The Transmuted Exponentiated Inverse Exponential (TEIE) Distribution has been derived using Exponentiated Inverse Exponential (EIE) distribution and the Quadratic Rank Transmutation Map (QRTM). The developed distribution is more flexible and adaptable in modeling data exhibiting different shapes of the hazard function than its sub-models. The mathematical expressions and shapes of the distribution function, probability density function, hazard rate function and reliability function are studied. The parameters of the TEIE distribution are estimated by the method of maximum likelihood. Finally, the TEIE distribution is applied to breast cancer data set and found to have a better fit than the Transmuted Inverse Exponential (EIE) distribution and the Inverse Exponential (IE) distribution.
References
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[3] Ogunde, A. A., Fayose, S. T., Ajayi, B., and Omosigho, D. O. "Properties, Inference, and Applications of Alpha Power Extended Inverted Weibull Distribution". International Journal of Statistics and Probability 9.6 (2020).
[4] Ogunde, A. A., Fatoki, O. and Oseghale, O. I. (2017a). "On the Application of Transmuted Inverted Weibull distribution". Global Journal of Science Frontier Research 17. 6(2017).
[5] Arowolo, O. T., Ogunsanya, A. S., Ekum, M. I., Oguntola T. O., and Ukam, J. B. "Exponentiated Weibull Inverse Rayleigh distribution". International Journal of Mathematical Sciences and Optimization: Theory and Applications 9.1(2023), pp. 104-122.
[6] Oguntunde, P. E., Adebowale O. A., and Enahoro A. O. "On the Flexibility of the Transmuted Inverse Exponential Distribution". Proceedings of the World Congress on Engineering 2017 Vol I WCE 2017, July 5-7, 2017, London, U.K.
[7] Ogunde, A. A., Omosigho, D. O., and Ajayi, B. "Structural Properties of Marshall-Olkin Extended Inverse Exponential Distribution". Mathematical Theory and Modeling 10.2(2020).
[8] Adetunji, K. I. and Jolayemi, E. T. "The weighted Exponentiated inverted exponential distribution". International Journal of Statistics and Applied Mathematics 6.1(2021), pp.45-50.
[9] Laoye, V. E. "Type II Topp-Leone Exponentiated Exponential Distribution: Properties and Application to Failure data". International Journal of Mathematical Research 16.6(2025), pp.39-47.
[10] Ashour, S. K. and M. A. Eltehiwy, M. A. "Transmuted Lomax distribution". American Journal of Applied Mathematics and Statistics 1.6(2013), pp.121-127.
[11] Khan, M.S. and King, R. "Transmuted Generalized Inverse Weibull Distribution". Journal of Applied Statistical Science 20(2013), pp.15-31.
[12] Ahmad, A., Ahmad, S. P., and Ahmed, A. "Transmuted inverse Rayleigh distribution: A generalization of then inverse Rayleigh distribution". Mathematical Theory and Modeling 4.7(2014), pp.90-98.
[13] Merovci, F., and Puka, I. "Transmuted Pareto distribution". Probability Statistical Forum 07, (2007), pp. 1-11.
[14] Elbatal, I. "Transmuted Modified Inverse Weibull Distribution: A Generalization Of The Modified Inverse Weibull Probability Distribution". International Journal of Mathematical Archeive 4(2013),pp.117-129.
[15] Afify, A. Z., Nofal, Z. M. and Butt, N. S. "Transmuted complementary Weibull geometric distribution". Pakistan Journal of Statistics and Operation Research 10.4(2014), pp.435-454.
[16] Oguntunde, P. E. and Adejumo, A. O. "The transmuted inverse exponential distribution". International Journal Advance Statistics and Probability 3.1(2015), pp.1-7.
[17] Merovci, F. "Transmuted Rayleigh Distribution". Austrian Journal of Statistics, 42(2013), pp.21-32.
[18] Elbatal, I. and Aryal, G. On the transmuted additive Weibull distribution. Australian Journal of Statistics 42.2(2013), pp.117-132.
[19] Aryal, G.R. "Transmuted Log-Logistic Distribution". Journal of Statistics Application and Probability 2(2013), pp.11-20.
[20] Mahmoud, M.R. and Mandouh, R.M. (2013). Transmuted Frechet Distribution. Journal of Applied Science and Research, 9, 5553-5561.
[21] Afify, A.Z., Nofal, Z.M. and Yousof, H.M. "The Transmuted Weibull Lomax Distribution: Properties and Application". Pakistan Journal of Statistics and Operation research 11.2(2015), pp.135-152.
[22] Shaw, W.T., and Buckley, I.R.C. (2007). The Alchemy of Probability Distributions: Beyond Gram-Charlier & Cornish-Fisher Expansions, and Skew-Normal or Kurtotic-Normal Distributions. 2007, Research report.
[23] Aryal, G. R., and Tsokos, C. P. "Transmuted Weibull distribution: A generalization of the Weibull probability distribution". European Journal of Pure Applied Mathematics 4(2011), pp.89-102.
[24] Hussain, M. A. "Transmuted exponentiated gamma distribution: A generalization of the exponentiated gamma probability distribution". Applied Journal of Mathematical Science, 8.27(2014), pp.1297-1310.
[25] Lucena, S.E.F., Silva, A.H.A. and Cordeiro, G.M. "The Transmuted Generalized Gamma Distribution: Properties and Application". Journal of Data Science 13(2015), pp.187-206.
[26] Ogunde, A. A., Omosigho, D. O., and Fatoki, O. (2017). "On Statistical Properties of the Exponentiated Transmuted Inverted Weibull Distribution". Journal of Statistics: Advances in Theory and Applications 18.2(2017), pp.143-164.
[27] Ogunde, A. A., Ibraheem, A. G., Audu, A. T. "Performance rating of transmuted Nadarajah and Haghighi exponential distribution: an analytical approach". Journal of Statistics: Advances in Theory and Applications 17.2(2017), pp.137-151.
[28] Tahir, M.H., Cordeiro, G.M., Mansoor, M., Zubair, M. "The Weibull-Lomax distribution: properties and applications". Hacetepe Journal of Mathematics and Statistics 44(2015), pp.461-480.
Published
2025-05-30
How to Cite
Oseghale, O. I., & Laoye, V. E. (2025). A Note on Transmuted Exponentiated Inverse Exponential Distribution and Application to Breast Cancer Data. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2), 45 - 54. Retrieved from https://ijmso.unilag.edu.ng/article/view/2892
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