ON THE MODELING OF BIOMEDICAL DATA SETS WITH A NEW GENERALIZED EXPONENTIATED EXPONENTIAL DISTRIBUTION
A NEW GENERALIZED EXPONENTIATED EXPONENTIAL DISTRIBUTION
,
Abstract
Many experts in the field of distribution theory have focused on extending probability distributions utilizing extended families of continuous distributions to improve the modeling adaptability of the conventional probability distributions. This study introduced a brand-new, five-parameter generalized exponentiated exponential distribution, which is a continuous probability distribution. With the aid of the quantile function, moments, moment generating function, survival function, hazard function, mean, and median, among other mathematical and statistical aspects, the new distribution's shape was deduced and researched. It was also possible to derive the probability density function for the minimum and maximum order statistics for this distribution. The method of maximum likelihood estimate was used to produce a conventional estimation of the unknown parameters. A simulation study was carried out to assess the efficiency and consistency of the estimation method used. To evaluate the fit and adaptability of the new model, it was applied to four real-world datasets in the field of medicine. The analysis's findings demonstrated that the new model performs better than its counterparts and offers a better fit than the Topp-Leone exponentiated exponential (TLEtEx), Topp-Leone Kumaraswamy exponential (TLKEx), exponentiated exponential (EtEx), and exponential (Ex) distributions.
[1] Figueredo, A. J. and Wolf, P. S. A. (2009). Assortative pairing and life history strategy- a cross-cultural study. Human Nature, 20:317–330.
[2] Joachims J. Learning to Classify Text Using Support Vector Machines: Methods, Theory and Algorithms, Kluwer, 2002.
[3] Cordeiro, G. M., and de Castro, M., (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81, 7, 883–898.
[4] Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S. and Shahbaz, M. Q., (2016). Topp-Leone family of distributions: Some properties and application, Pakistan Journal of Statistics and Operation Research. XII, 3, 443-451.
[5] Elgarhy, M., Muhammad, A. H., Gamze, O. and Muhammad, A. N. (2017). A new exponentiated extended family of distributions with applications, Gazi University Journal of Science, 30(3): 101 – 115.
[6] Hassan, S. and Nassr, S.G., Power Lindley-G Family of Distributions, Annals of Data Science, 6: 189-210, (2019).
[7] Ibrahim, S., Doguwa, S.I., Audu, I. and Jibril, H.M., (2020). On the Topp Leone exponentiated-G Family of Distributions: Properties and Applications, Asian Journal of Probability and Statistics; 7(1): 1-15.
[8] Ibrahim, S., Doguwa S. I., Audu, I. and Jibril, H. M., (2020). The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data, Journal of Biostatistics and Epidemiology, 6(1):37-48.
[9] Anzagra, L., Sarpong, S. and Nasiru, S., (2020). Odd Chen-G family of distributions, Annals of Data Science, doi.org/10.1007/s40745-020-00248-2.
[10] Modi, K., Kumar, D. and Singh, Y., (2020). A New Family of Distribution with Application on Two Real Data sets on Survival Problem, Science and Technology Asia, 25(1): 1-10.
[11] Rasheed, N. (2020). A new generalized-G class of distributions and its applications with Dagun distribution. Research Journal of Mathematical and Statistical Science, 8(3), 1-13.
[12] Bello, O. A., Doguwa, S. I., Yahaya, A. and Jibril, H. M. (2020). A type I half Logistic exponentiated-G family of distributions: Properties and application, Communication in Physical Sciences, 7(3): 147 – 163.
[13] Bello, O. A., Doguwa, S. I., Yahaya, A. and Jibril, H. M. (2021). A type II half Logistic exponentiated-G family of distributions with applications to survival analysis, FUDMA Journal of Sciences, 7(3): 147-163.
[14] Yousof, H. M., Alizadeh, M., Jahanshahiand, S. M. A., Ramires, T. G., Ghosh, I. and Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15(4): 723–740.
[15] Almutiry, W., Alahmadi, A. A., Elbatal, I., Ragab, I. E., Balogun, O. S. and Elgarhy, M. (2021). Application to Engineering and Medical Data Using Three-Parameter Exponential Model, Mobile Information Systems, vol. 2021, Article ID 9550156, 14 pages. https://doi.org/10.1155/2021/9550156
[16] Aldahlan, M. A. D. and Afify, A. Z. (2020). The odd exponentiated half-logistic exponential distribution: estimation methods and application to engineering data, Mathematics, 8(10), Article ID 1684.
[17] Aldahlan, M. A. D. and Afify, A. Z. (2020). A new three-parameter exponential distribution with applications in reliability and engineering, The Journal of Nonlinear Science and Applications, 13(5): 258-269.
[18] Ibrahim, M. and Yousof, H. (2020). Transmuted Topp-Leone Weibull lifetime distribution: statistical properties and different method of estimation, Pakistan Journal of Statistics and Operation Research, 16, 501–515.
[19] Gupta, R. D. and Kundu, D., (1999). Generalized Exponential Distributions, Australian and New Zealand Journal of Statistics, 41(2): 173-188.
[20] Gupta, R. D. and Kundu, D., (2001a). Exponentiated Exponential Family: An Alternative to Gamma and Weibull, Biometrical Journal, 33(1): 117-130.
[21] Gupta, R.D. and Kundu, D. (2001b). Generalized Exponential Distributions: Different Methods of Estimation, Journal of Statistical Computation and Simulation, 69(4): 315-338.
[22] Gupta, R. D. and Kundu, D. (2003). Discriminating Between the Weibull and the GE Distributions, Computational Statistics and Data Analysis, 43, 179-196.
[23] Gupta, R. D. and Kundu, D. (2004). Discriminating Between the Gamma and Generalized Exponential Distributions, Journal of Statistical Computation and Simulation, 74(2): 107-121.
[24] Gupta, R. D. and Kundu, D. (2007). Generalized exponential distribution: existing methods and recent developments, Journal of the Statistical Planning and Inference, 137(11): 3537 – 3547.
[25] Gross, A. J. and Clark, V. A. (1975). Survival distributions: reliability applications in the biometrical sciences, John Wiley and Sons, Inc., New York.
[26] Hosseini, B., Afshari, M. and Alizadeh M. (2018). The generalized odd gamma-G family of distributions: properties and applications. Austrian Journal of Statistics, 47(2):69-89
[27] Lee, E. T. and Wang, J. W: Statistical methods for survival data analysis (3rd Edition), John Wiley and Sons, New York, USA, 535 Pages,(2003) ISBN 0-471-36997-7.
[28] Lee, E. T. (1992). Statistical methods for survival data analysis (2nd Edition), John Wiley and Sons Inc., New York, USA, 156 Pages.
[2] Joachims J. Learning to Classify Text Using Support Vector Machines: Methods, Theory and Algorithms, Kluwer, 2002.
[3] Cordeiro, G. M., and de Castro, M., (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81, 7, 883–898.
[4] Al-Shomrani, A., Arif, O., Shawky, A., Hanif, S. and Shahbaz, M. Q., (2016). Topp-Leone family of distributions: Some properties and application, Pakistan Journal of Statistics and Operation Research. XII, 3, 443-451.
[5] Elgarhy, M., Muhammad, A. H., Gamze, O. and Muhammad, A. N. (2017). A new exponentiated extended family of distributions with applications, Gazi University Journal of Science, 30(3): 101 – 115.
[6] Hassan, S. and Nassr, S.G., Power Lindley-G Family of Distributions, Annals of Data Science, 6: 189-210, (2019).
[7] Ibrahim, S., Doguwa, S.I., Audu, I. and Jibril, H.M., (2020). On the Topp Leone exponentiated-G Family of Distributions: Properties and Applications, Asian Journal of Probability and Statistics; 7(1): 1-15.
[8] Ibrahim, S., Doguwa S. I., Audu, I. and Jibril, H. M., (2020). The Topp Leone Kumaraswamy-G Family of Distributions with Applications to Cancer Disease Data, Journal of Biostatistics and Epidemiology, 6(1):37-48.
[9] Anzagra, L., Sarpong, S. and Nasiru, S., (2020). Odd Chen-G family of distributions, Annals of Data Science, doi.org/10.1007/s40745-020-00248-2.
[10] Modi, K., Kumar, D. and Singh, Y., (2020). A New Family of Distribution with Application on Two Real Data sets on Survival Problem, Science and Technology Asia, 25(1): 1-10.
[11] Rasheed, N. (2020). A new generalized-G class of distributions and its applications with Dagun distribution. Research Journal of Mathematical and Statistical Science, 8(3), 1-13.
[12] Bello, O. A., Doguwa, S. I., Yahaya, A. and Jibril, H. M. (2020). A type I half Logistic exponentiated-G family of distributions: Properties and application, Communication in Physical Sciences, 7(3): 147 – 163.
[13] Bello, O. A., Doguwa, S. I., Yahaya, A. and Jibril, H. M. (2021). A type II half Logistic exponentiated-G family of distributions with applications to survival analysis, FUDMA Journal of Sciences, 7(3): 147-163.
[14] Yousof, H. M., Alizadeh, M., Jahanshahiand, S. M. A., Ramires, T. G., Ghosh, I. and Hamedani, G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science, 15(4): 723–740.
[15] Almutiry, W., Alahmadi, A. A., Elbatal, I., Ragab, I. E., Balogun, O. S. and Elgarhy, M. (2021). Application to Engineering and Medical Data Using Three-Parameter Exponential Model, Mobile Information Systems, vol. 2021, Article ID 9550156, 14 pages. https://doi.org/10.1155/2021/9550156
[16] Aldahlan, M. A. D. and Afify, A. Z. (2020). The odd exponentiated half-logistic exponential distribution: estimation methods and application to engineering data, Mathematics, 8(10), Article ID 1684.
[17] Aldahlan, M. A. D. and Afify, A. Z. (2020). A new three-parameter exponential distribution with applications in reliability and engineering, The Journal of Nonlinear Science and Applications, 13(5): 258-269.
[18] Ibrahim, M. and Yousof, H. (2020). Transmuted Topp-Leone Weibull lifetime distribution: statistical properties and different method of estimation, Pakistan Journal of Statistics and Operation Research, 16, 501–515.
[19] Gupta, R. D. and Kundu, D., (1999). Generalized Exponential Distributions, Australian and New Zealand Journal of Statistics, 41(2): 173-188.
[20] Gupta, R. D. and Kundu, D., (2001a). Exponentiated Exponential Family: An Alternative to Gamma and Weibull, Biometrical Journal, 33(1): 117-130.
[21] Gupta, R.D. and Kundu, D. (2001b). Generalized Exponential Distributions: Different Methods of Estimation, Journal of Statistical Computation and Simulation, 69(4): 315-338.
[22] Gupta, R. D. and Kundu, D. (2003). Discriminating Between the Weibull and the GE Distributions, Computational Statistics and Data Analysis, 43, 179-196.
[23] Gupta, R. D. and Kundu, D. (2004). Discriminating Between the Gamma and Generalized Exponential Distributions, Journal of Statistical Computation and Simulation, 74(2): 107-121.
[24] Gupta, R. D. and Kundu, D. (2007). Generalized exponential distribution: existing methods and recent developments, Journal of the Statistical Planning and Inference, 137(11): 3537 – 3547.
[25] Gross, A. J. and Clark, V. A. (1975). Survival distributions: reliability applications in the biometrical sciences, John Wiley and Sons, Inc., New York.
[26] Hosseini, B., Afshari, M. and Alizadeh M. (2018). The generalized odd gamma-G family of distributions: properties and applications. Austrian Journal of Statistics, 47(2):69-89
[27] Lee, E. T. and Wang, J. W: Statistical methods for survival data analysis (3rd Edition), John Wiley and Sons, New York, USA, 535 Pages,(2003) ISBN 0-471-36997-7.
[28] Lee, E. T. (1992). Statistical methods for survival data analysis (2nd Edition), John Wiley and Sons Inc., New York, USA, 156 Pages.
| Files | ||
| Issue | Vol 9 No 4 (2023) | |
| Section | Articles | |
| DOI | https://doi.org/10.18502/jbe.v9i4.16673 | |
| Keywords | ||
| skewness kurtosis biomedical exponentiated exponential | ||
| Rights and permissions | |
|
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
How to Cite
1.
Sule I, Ismail K, Bello O. ON THE MODELING OF BIOMEDICAL DATA SETS WITH A NEW GENERALIZED EXPONENTIATED EXPONENTIAL DISTRIBUTION. JBE. 2023;9(4):484- 499.
