Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates

Abeer Mohamed; Amira Elghany; Gamalat Elgabry

doi:doi:10.11648/j.sjams.20210902.12

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Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates

Abeer Mohamed, Amira Elghany, Gamalat Elgabry

Published in Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 2)

Received: 1 March 2021 Accepted: 17 March 2021 Published: 30 March 2021

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Abstract

In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 9, Issue 2)
DOI	10.11648/j.sjams.20210902.12
Page(s)	44-56
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.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Power Odd Generalized Exponential-Gompertez Distribution, Maximum Likelihood Estimation, Maximum Product Spacing, Bayesian Estimation, Metropolis-Hasting Algorithm, Mortality Rates in Egypt

References

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[2]	Alizadeh, M.; Afify, A. Z.; Eliwa, M. & Ali, S. (2020). The odd log-logistic Lindley-G family of distributions: Properties, Bayesian and non-Bayesian estimation with applications. Comput. Stat. 35, 281–308.
[3]	Ashour, S. K. and Eltehiwy, M. A. (2015). Exponentiated power Lindley distribution. Journal of advanced research, 6 (6), 895-905.‏ doi: 10.1016/j.jare.2014.08.005.
[4]	Anatolyev, S. and Kosenok, G. (2005). An Alternative to Maximum likelihood based on Spacings. Econometric Theory, 21 (2), 472-476.
[5]	Chesneau, C & Djlbrila, S. (2019). The Generalized Odd Inverted Exponential-G family of Distributions: Properties and Applications. Eurasian Bulletin of Mathematics (ISSN: 2687-5632), [S.l.], 2 (3), 86-110. ISSN 2687-5632.
[6]	Cheng, R. C. H, & Amin, N. A. K. (1983). Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin. Journal of the Royal Statistical Society. Series B Methodological, 45 (3): 394–403. Doi: 10.1111/j.2517-6161.1983.tb01268.x.
[7]	Chen, M. H. and Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8, 69–92.
[8]	Cordeiro, G. M.; Afify, A. Z.; Ortega, E. M.; Suzuki, A. K. & Mead, M. E. (2019) The odd Lomax generator of distributions: Properties, estimation and applications. J. Comput. Appl. Math. 347, 222–237.
[9]	Dey, S. and Pradhan, B. (2014). Generalized inverted exponential distribution under hybrid censoring. Statistical Methodology, 18, 101-114.
[10]	El-Bassiouny, A. H, Abdo, N. F & Shahen. H. S. (2015). Exponential Lomax distribution. International Journal Computer Applications, 121 (13): 24-29.
[11]	El-Damcese, M. A. Mustafa, A., El-Desouky. B. S. and Mustafa M. E. (2015). The Odd Generalized Exponential Gompertz. Journal of Applied Mathematics, vol. 6, 2340-2353.
[12]	Ghitany, M., Al-Mutairi, D., Balakrishnan, N., and Al-Enezi, I. (2013). Power lindley distribution and associated inference. Computational Statistics and Data Analysis64: 20-33.
[13]	Hassan, A. S. & M. Abd-Alla, 2018. Exponentiated Weibull Lomax: Properties and estimation. J. Data Sci., 16: 277-298.
[14]	Pararai, Marvis, Gayan Warahena-Liyanage and Broderick O. Oluyede. (2015). "A New Class of Generalized Power Lindley Distribution with Applications to Lifetime Data." Theoretical Mathematics and Applications, 5 (1), 53-96.
[15]	Ravenzwaaij, D. v., Cassey, P. and Brown, S. D. (2016). A simple introduction to Markov Chain Monte–Carlo sampling. Psychonomic Bulletin Review, 25, 143-154.

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APA Style

Abeer Mohamed, Amira Elghany, Gamalat Elgabry. (2021). Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Science Journal of Applied Mathematics and Statistics, 9(2), 44-56. https://doi.org/10.11648/j.sjams.20210902.12

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ACS Style

Abeer Mohamed; Amira Elghany; Gamalat Elgabry. Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Sci. J. Appl. Math. Stat. 2021, 9(2), 44-56. doi: 10.11648/j.sjams.20210902.12

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AMA Style

Abeer Mohamed, Amira Elghany, Gamalat Elgabry. Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Sci J Appl Math Stat. 2021;9(2):44-56. doi: 10.11648/j.sjams.20210902.12

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@article{10.11648/j.sjams.20210902.12,
  author = {Abeer Mohamed and Amira Elghany and Gamalat Elgabry},
  title = {Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {2},
  pages = {44-56},
  doi = {10.11648/j.sjams.20210902.12},
  url = {https://doi.org/10.11648/j.sjams.20210902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210902.12},
  abstract = {In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.},
 year = {2021}
}

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TY  - JOUR
T1  - Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates
AU  - Abeer Mohamed
AU  - Amira Elghany
AU  - Gamalat Elgabry
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210902.12
DO  - 10.11648/j.sjams.20210902.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 44
EP  - 56
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210902.12
AB  - In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.
VL  - 9
IS  - 2
ER  -

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Author Information

Abeer Mohamed

Department of Statistics, Faculty of Commerce, AL-Azhar University, Cairo, Egypt
Amira Elghany

Department of Statistics, Faculty of Commerce, AL-Azhar University, Cairo, Egypt
Gamalat Elgabry

Department of Statistics, Faculty of Commerce, AL-Azhar University, Cairo, Egypt

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Plain Text BibTeX RIS

APA Style

Abeer Mohamed, Amira Elghany, Gamalat Elgabry. (2021). Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Science Journal of Applied Mathematics and Statistics, 9(2), 44-56. https://doi.org/10.11648/j.sjams.20210902.12

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ACS Style

Abeer Mohamed; Amira Elghany; Gamalat Elgabry. Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Sci. J. Appl. Math. Stat. 2021, 9(2), 44-56. doi: 10.11648/j.sjams.20210902.12

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AMA Style

Abeer Mohamed, Amira Elghany, Gamalat Elgabry. Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates. Sci J Appl Math Stat. 2021;9(2):44-56. doi: 10.11648/j.sjams.20210902.12

Copy | Download

@article{10.11648/j.sjams.20210902.12,
  author = {Abeer Mohamed and Amira Elghany and Gamalat Elgabry},
  title = {Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {9},
  number = {2},
  pages = {44-56},
  doi = {10.11648/j.sjams.20210902.12},
  url = {https://doi.org/10.11648/j.sjams.20210902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20210902.12},
  abstract = {In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Estimating the Parameters of (POGE-G) Distribution and Its Application to Egyptian Mortality Rates
AU  - Abeer Mohamed
AU  - Amira Elghany
AU  - Gamalat Elgabry
Y1  - 2021/03/30
PY  - 2021
N1  - https://doi.org/10.11648/j.sjams.20210902.12
DO  - 10.11648/j.sjams.20210902.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 44
EP  - 56
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20210902.12
AB  - In this paper, we consider power odd generalized exponential-Gompertz (POGE-G) distribution which is capable of life tables to calculate death rates (failure). Based on simulated data from the PPOGE-G distribution, we consider the problem of estimation of parameters under classical approaches and Bayesian approaches. In this regard, we obtain maximum likelihood (ML) estimates, maximum product of spacing (MPS) and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates. The Monte Carlo simulation will be conduct to study and compare the performance of the various proposed estimators (simulation study indicates that the performance of MPS estimates is better MLE estimates and the performance of Bayes estimates is also better). Finally, application of a real data from the projections of the future population for the total of the Egyptian Arabic Republic for the period 2017-2052, depending on the book which introduced from the central agency for public mobilization and statistics in Feb (2019) from this application it could be said that this distributions can be applied to mortality rate data set. The present paper can also be extended to design of progressive censoring sampling plan and other censoring schemes can also be considered.
VL  - 9
IS  - 2
ER  -

Copy | Download