We developed a five parameter distribution known as the Generalized Exponentiated Gompertz Makeham distribution which is quite flexible and can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters making it more effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density function, cumulative distribution function, hazard rate function, moment generating function and order Statistics were provided as well as maximum likelihood estimation of the Generalized Exponentiated Gompertz Makeham distribution parameters and at the end, in order to show the distribution flexibility, an application using a real data set was presented.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5) |
| DOI | 10.11648/j.ajtas.20170605.12 |
| Page(s) | 228-235 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Generalized Exponentiated Gompertz Makeham Distribution, Maximum Likelihood Estimation, Bathtub-Shape Failure Rate, Distribution Flexibility
| [1] | Bailey RC (1978) Limiting form of the Makeham model and their use for survival analysis of transplant studies. Biometries 34: 725-726. |
| [2] | Bourguignon, M., R. B. Silva, L. M. Zea and G. M. Cordeiro, 2013. The Kumaraswamy Pareto distribution. J. of Stat. Theory and Applications, 12: 129-144. |
| [3] | Cordeiro, G. M., E. M. M. Ortega and Daniel C. C da Cunha. The Exponentiated Generalized Class of Distributions. Journal of Data Science 11(2013), 1-27. |
| [4] | Cordeiro, G. M. and M. de Castro, 2010. A new family of generalized distributions. Journal of Statistical Computation and Simulation, 81: 883-898. |
| [5] | Cordeiro, G. M., et al. The Exponentiated Generalized Class of Distributions. Journal of Data Science 11(2013), 1-27. |
| [6] | Chukwu A. U. & Ogunde A. A. (2015), 'On the Beta Makeham Distribution and its Applications', American Journal of Mathematics and Statistics 2015, 5(3): 137-143. |
| [7] | El-Gohary, A. & Al-Otaibi, A. N. (2013), ‘The generalized Gompertz distribution’, Applied Mathematical Modeling 37(1-2), 13–24. |
| [8] | Finch CE. Chicago: University of Chicago Press; 1990. Longevity. Senescence, and the Genome. |
| [9] | Gupta, R. C., Gupta, P. L. and Gupta, R. D. (1998). Modeling failure time data by Lehmann alternatives. Communications in Statistics - Theory and Methods 27, 887-904. |
| [10] | Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics 41, 173-188. |
| [11] | Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family: an alternative to gamma and Weibull. Biometrical Journal 43, 117-130. |
| [12] | Gompertz, B. (1825). "On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society 115: 513–585. doi:10.1098/rstl.1825.0026. |
| [13] | Jodra, P. (2009). "A closed form expression for the quantile functions of the Gompertz Makeham distribution". Mathematics and Computers in Simulation 79 (10): 3069–3075. doi:10.1016/j.matcom.2009.02.002. |
| [14] | Lehmann, E. L. (1953). The power of rank tests. Annals of Mathematical Statistics 24, 23-43. Shahbaz, M. Q., S. Shahbaz and N. S. Butt, 2012. The Kumaraswamy inverse Weibull distribution. Pakistan Journal of Statistics and Operation Research, 8: 479-489. |
| [15] | Makeham, W. M. (1860). "On the Law of Mortality and the Construction of Annuity Tables". J. Inst. Actuaries and Assurance. Mag. 8: 301–310. |
| [16] | Nadarajah, S., and Kotz, S. (2005). The beta exponential distribution. Reliability Engineering and System Safety, 91, 689-697. |
| [17] | Souza, W. M., G. M. Cordeiro and A. B. Simas, 2011. Some results for beta Fréchet distribution. Commun. Statist. Theory-Meth., 40: 798-811. |
| [18] | Zografos, K. and N. Balakrishnan, 2009. On families of beta- and generalized gamma-generated distributions and associated inference. Stat. Method., 6: 344-362. s. |
APA Style
Ogunde Adebisi Ade, Fatoki Olayode, Ajayi Bamidele. (2017). Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach. American Journal of Theoretical and Applied Statistics, 6(5), 228-235. https://doi.org/10.11648/j.ajtas.20170605.12
ACS Style
Ogunde Adebisi Ade; Fatoki Olayode; Ajayi Bamidele. Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach. Am. J. Theor. Appl. Stat. 2017, 6(5), 228-235. doi: 10.11648/j.ajtas.20170605.12
AMA Style
Ogunde Adebisi Ade, Fatoki Olayode, Ajayi Bamidele. Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach. Am J Theor Appl Stat. 2017;6(5):228-235. doi: 10.11648/j.ajtas.20170605.12
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Download@article{10.11648/j.ajtas.20170605.12,
author = {Ogunde Adebisi Ade and Fatoki Olayode and Ajayi Bamidele},
title = {Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {5},
pages = {228-235},
doi = {10.11648/j.ajtas.20170605.12},
url = {https://doi.org/10.11648/j.ajtas.20170605.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170605.12},
abstract = {We developed a five parameter distribution known as the Generalized Exponentiated Gompertz Makeham distribution which is quite flexible and can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters making it more effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density function, cumulative distribution function, hazard rate function, moment generating function and order Statistics were provided as well as maximum likelihood estimation of the Generalized Exponentiated Gompertz Makeham distribution parameters and at the end, in order to show the distribution flexibility, an application using a real data set was presented.},
year = {2017}
}
TY - JOUR T1 - Performance Rating of the Exponentiated Generalized Gompertz Makeham Distribution: An Analytical Approach AU - Ogunde Adebisi Ade AU - Fatoki Olayode AU - Ajayi Bamidele Y1 - 2017/09/04 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.20170605.12 DO - 10.11648/j.ajtas.20170605.12 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 228 EP - 235 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20170605.12 AB - We developed a five parameter distribution known as the Generalized Exponentiated Gompertz Makeham distribution which is quite flexible and can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters making it more effective in modeling survival data and reliability problems. Some comprehensive properties of the new distribution, such as closed-form expressions for the density function, cumulative distribution function, hazard rate function, moment generating function and order Statistics were provided as well as maximum likelihood estimation of the Generalized Exponentiated Gompertz Makeham distribution parameters and at the end, in order to show the distribution flexibility, an application using a real data set was presented. VL - 6 IS - 5 ER -
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