Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior

Mohamed Maswadah; Seham Mohamed

doi:doi:10.11648/j.sjams.20241202.12

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Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior

Mohamed Maswadah

, Seham Mohamed^*

Published in Science Journal of Applied Mathematics and Statistics (Volume 12, Issue 2)

Received: 6 April 2024 Accepted: 22 April 2024 Published: 17 May 2024

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Abstract

In this work, we introduce an objective prior based on the kernel density estimation to eliminate the subjectivity of the Bayesian estimation for information other than data. For comparing the kernel prior with the informative gamma prior, the mean squared error and the mean percentage error for the generalized exponential (GE) distribution parameters estimations are studied using both symmetric and asymmetric loss functions via Monte Carlo simulations. The simulation results indicated that the kernel prior outperforms the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 12, Issue 2)
DOI	10.11648/j.sjams.20241202.12
Page(s)	29-36
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

Informative Prior, Kernel Prior, LINEX Loss Function, Squared Error Loss Function

References

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APA Style

Maswadah, M., Mohamed, S. (2024). Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Science Journal of Applied Mathematics and Statistics, 12(2), 29-36. https://doi.org/10.11648/j.sjams.20241202.12

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ACS Style

Maswadah, M.; Mohamed, S. Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Sci. J. Appl. Math. Stat. 2024, 12(2), 29-36. doi: 10.11648/j.sjams.20241202.12

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AMA Style

Maswadah M, Mohamed S. Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Sci J Appl Math Stat. 2024;12(2):29-36. doi: 10.11648/j.sjams.20241202.12

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@article{10.11648/j.sjams.20241202.12,
  author = {Mohamed Maswadah and Seham Mohamed},
  title = {Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior
},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {12},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.sjams.20241202.12},
  url = {https://doi.org/10.11648/j.sjams.20241202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20241202.12},
  abstract = {In this work, we introduce an objective prior based on the kernel density estimation to eliminate the subjectivity of the Bayesian estimation for information other than data. For comparing the kernel prior with the informative gamma prior, the mean squared error and the mean percentage error for the generalized exponential (GE) distribution parameters estimations are studied using both symmetric and asymmetric loss functions via Monte Carlo simulations. The simulation results indicated that the kernel prior outperforms the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.
},
 year = {2024}
}

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TY  - JOUR
T1  - Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior

AU  - Mohamed Maswadah
AU  - Seham Mohamed
Y1  - 2024/05/17
PY  - 2024
N1  - https://doi.org/10.11648/j.sjams.20241202.12
DO  - 10.11648/j.sjams.20241202.12
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  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20241202.12
AB  - In this work, we introduce an objective prior based on the kernel density estimation to eliminate the subjectivity of the Bayesian estimation for information other than data. For comparing the kernel prior with the informative gamma prior, the mean squared error and the mean percentage error for the generalized exponential (GE) distribution parameters estimations are studied using both symmetric and asymmetric loss functions via Monte Carlo simulations. The simulation results indicated that the kernel prior outperforms the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.

VL  - 12
IS  - 2
ER  -

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Author Information

Mohamed Maswadah

Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt

Contact Email

http://orcid.org/0000-0002-2296-931X
Seham Mohamed

Department of Mathematics, Faculty of Science, Aswan University, Aswan, Egypt

Contact Email

http://orcid.org/0000-0002-5966-4632

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APA Style

Maswadah, M., Mohamed, S. (2024). Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Science Journal of Applied Mathematics and Statistics, 12(2), 29-36. https://doi.org/10.11648/j.sjams.20241202.12

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ACS Style

Maswadah, M.; Mohamed, S. Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Sci. J. Appl. Math. Stat. 2024, 12(2), 29-36. doi: 10.11648/j.sjams.20241202.12

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AMA Style

Maswadah M, Mohamed S. Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior. Sci J Appl Math Stat. 2024;12(2):29-36. doi: 10.11648/j.sjams.20241202.12

Copy | Download

@article{10.11648/j.sjams.20241202.12,
  author = {Mohamed Maswadah and Seham Mohamed},
  title = {Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior
},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {12},
  number = {2},
  pages = {29-36},
  doi = {10.11648/j.sjams.20241202.12},
  url = {https://doi.org/10.11648/j.sjams.20241202.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20241202.12},
  abstract = {In this work, we introduce an objective prior based on the kernel density estimation to eliminate the subjectivity of the Bayesian estimation for information other than data. For comparing the kernel prior with the informative gamma prior, the mean squared error and the mean percentage error for the generalized exponential (GE) distribution parameters estimations are studied using both symmetric and asymmetric loss functions via Monte Carlo simulations. The simulation results indicated that the kernel prior outperforms the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Bayesian Inference on the Generalized Exponential Distribution Based on the Kernel Prior

AU  - Mohamed Maswadah
AU  - Seham Mohamed
Y1  - 2024/05/17
PY  - 2024
N1  - https://doi.org/10.11648/j.sjams.20241202.12
DO  - 10.11648/j.sjams.20241202.12
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  - 29
EP  - 36
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20241202.12
AB  - In this work, we introduce an objective prior based on the kernel density estimation to eliminate the subjectivity of the Bayesian estimation for information other than data. For comparing the kernel prior with the informative gamma prior, the mean squared error and the mean percentage error for the generalized exponential (GE) distribution parameters estimations are studied using both symmetric and asymmetric loss functions via Monte Carlo simulations. The simulation results indicated that the kernel prior outperforms the informative gamma prior. Finally, a numerical example is given to demonstrate the efficiency of the proposed priors.

VL  - 12
IS  - 2
ER  -

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