Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey

Afriani; Ardi Kurniawan; Elly Ana

doi:doi:10.11648/j.ijsd.20230902.12

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Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey

Afriani, Ardi Kurniawan, Elly Ana

Published in International Journal of Statistical Distributions and Applications (Volume 9, Issue 2)

Received: 11 June 2023 Accepted: 4 July 2023 Published: 11 July 2023

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Abstract

Lifetime data analysis or survival analysis is a technique in statistics that can be used to test the durability and reliability of a component. The life time data obtained from the life test experiment is in the form of type I censored data if the life test data is generated after the experiment lasts for a predetermined time. This study aims to obtain a parameter estimator from the exponential distribution of type I censored data using the Linear Exponential Loss Function (LINEX) method. The prior distribution used in this study is a non-informative prior with the technique of determining it using the Jeffrey method. So that the research results were obtained in the form of a parameter estimator θ is Furthermore, applied to secondary data on the survival time of patients with chronic kidney failure at one of the Bojonegoro Hospitals was carried out in 2014. The data is divided into two, namely data on patients with initial causes of diabetic (data 1) and non-diabetic (data 2) diseases. Based on the estimation results for case studies of patients with chronic kidney failure, the value = 0.0102608 for patients with initial causes of diabetic disease and = 0.00712166 for patients with initial causes of non-diabetic disease. This shows that the possibility of patients with initial causes of diabetic disease to fail (die) is higher than patients with non-diabetic causes of disease.

Published in	International Journal of Statistical Distributions and Applications (Volume 9, Issue 2)
DOI	10.11648/j.ijsd.20230902.12
Page(s)	62-67
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

Exponential Distribution, Prior Jeffrey, Bayesian Method, LINEX Loss Function

References

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[8]	Bolstad, W. M. (2007), Introduction to Bayesian Statistics, 2nd edition. New Jersey: John Wiley & Sons, Inc.
[9]	Varian, H. R. (1975), A Bayesian approach to real estate assessment. In Studies in Bayesian Econometrics and Statist ics in Honor of Leonard J. Savage, eds. Stephan E. Fienberg and Arnold Zellner, Amsterdam: NorthHolland, pp. 195-208.
[10]	Ramadhan, R. A., Rahayu, W., & Hadi, I. (2022), Bayesian Method for Estimating Exponential Distribution Parameters on Censored Data, Journal of Applied and Mathematics, 4, 20-26.
[11]	Puspitawati, D., Rizki, S. W., & Imro’ah, N. (2019), Bayesian SELF and Bayesian GELF Method Approaches for Parameter Estimation of Exponential Survival Models with Prior Jeffreys, The Math Scientific Bulletin. Stats. and Applied, 3, 407-414.
[12]	Sagita, I., Setyahadewi, N., & Rizki, W. R. (2018), Comparison of the LINEX Bayesian Method on the Estimation of Survival Model Parameters of the Weibull Distribution of Censored Data, The Math Scientific Bulletin. Stats. and Applied, 7 (4), 353-362.
[13]	Ahmed, A., Ahmad, S. P., & Reshi, J. A. (2013), Bayesian analysis of Rayleigh distribution. International Journal of Scientific and Research Publications, 3 (10), 1–9.
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[16]	Putri, N. H. (2016), Endurance modeling of chronic kidney failure patients undergoing hemodialysis therapy in Bojonegoro using the Multivariate Adaptive Regression Spline method (MARS) (Thesis), Airlangga University, Surabaya.
[17]	Ariwicaksono, dr. Stefanus Cahyo. (2023), Be careful! Diabetes & Hypertension Causing Chronic Kidney Failure, https://www.siloamhospitals.com/informasi-siloam/artikel/penyebab-gagal-ginjal-kronis, June 2, 2023.

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APA Style

Afriani, Ardi Kurniawan, Elly Ana. (2023). Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. International Journal of Statistical Distributions and Applications, 9(2), 62-67. https://doi.org/10.11648/j.ijsd.20230902.12

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ACS Style

Afriani; Ardi Kurniawan; Elly Ana. Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. Int. J. Stat. Distrib. Appl. 2023, 9(2), 62-67. doi: 10.11648/j.ijsd.20230902.12

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AMA Style

Afriani, Ardi Kurniawan, Elly Ana. Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. Int J Stat Distrib Appl. 2023;9(2):62-67. doi: 10.11648/j.ijsd.20230902.12

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@article{10.11648/j.ijsd.20230902.12,
  author = {Afriani and Ardi Kurniawan and Elly Ana},
  title = {Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {2},
  pages = {62-67},
  doi = {10.11648/j.ijsd.20230902.12},
  url = {https://doi.org/10.11648/j.ijsd.20230902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230902.12},
  abstract = {Lifetime data analysis or survival analysis is a technique in statistics that can be used to test the durability and reliability of a component. The life time data obtained from the life test experiment is in the form of type I censored data if the life test data is generated after the experiment lasts for a predetermined time. This study aims to obtain a parameter estimator from the exponential distribution of type I censored data using the Linear Exponential Loss Function (LINEX) method. The prior distribution used in this study is a non-informative prior with the technique of determining it using the Jeffrey method. So that the research results were obtained in the form of a parameter estimator θ is  Furthermore, applied to secondary data on the survival time of patients with chronic kidney failure at one of the Bojonegoro Hospitals was carried out in 2014. The data is divided into two, namely data on patients with initial causes of diabetic (data 1) and non-diabetic (data 2) diseases. Based on the estimation results for case studies of patients with chronic kidney failure, the value  = 0.0102608 for patients with initial causes of diabetic disease and  = 0.00712166 for patients with initial causes of non-diabetic disease. This shows that the possibility of patients with initial causes of diabetic disease to fail (die) is higher than patients with non-diabetic causes of disease.},
 year = {2023}
}

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TY  - JOUR
T1  - Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey
AU  - Afriani
AU  - Ardi Kurniawan
AU  - Elly Ana
Y1  - 2023/07/11
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230902.12
DO  - 10.11648/j.ijsd.20230902.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 62
EP  - 67
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230902.12
AB  - Lifetime data analysis or survival analysis is a technique in statistics that can be used to test the durability and reliability of a component. The life time data obtained from the life test experiment is in the form of type I censored data if the life test data is generated after the experiment lasts for a predetermined time. This study aims to obtain a parameter estimator from the exponential distribution of type I censored data using the Linear Exponential Loss Function (LINEX) method. The prior distribution used in this study is a non-informative prior with the technique of determining it using the Jeffrey method. So that the research results were obtained in the form of a parameter estimator θ is  Furthermore, applied to secondary data on the survival time of patients with chronic kidney failure at one of the Bojonegoro Hospitals was carried out in 2014. The data is divided into two, namely data on patients with initial causes of diabetic (data 1) and non-diabetic (data 2) diseases. Based on the estimation results for case studies of patients with chronic kidney failure, the value  = 0.0102608 for patients with initial causes of diabetic disease and  = 0.00712166 for patients with initial causes of non-diabetic disease. This shows that the possibility of patients with initial causes of diabetic disease to fail (die) is higher than patients with non-diabetic causes of disease.
VL  - 9
IS  - 2
ER  -

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Author Information

Afriani

Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya, Indonesia
Ardi Kurniawan

Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya, Indonesia
Elly Ana

Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya, Indonesia

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Plain Text BibTeX RIS

APA Style

Afriani, Ardi Kurniawan, Elly Ana. (2023). Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. International Journal of Statistical Distributions and Applications, 9(2), 62-67. https://doi.org/10.11648/j.ijsd.20230902.12

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ACS Style

Afriani; Ardi Kurniawan; Elly Ana. Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. Int. J. Stat. Distrib. Appl. 2023, 9(2), 62-67. doi: 10.11648/j.ijsd.20230902.12

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AMA Style

Afriani, Ardi Kurniawan, Elly Ana. Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey. Int J Stat Distrib Appl. 2023;9(2):62-67. doi: 10.11648/j.ijsd.20230902.12

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@article{10.11648/j.ijsd.20230902.12,
  author = {Afriani and Ardi Kurniawan and Elly Ana},
  title = {Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {9},
  number = {2},
  pages = {62-67},
  doi = {10.11648/j.ijsd.20230902.12},
  url = {https://doi.org/10.11648/j.ijsd.20230902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20230902.12},
  abstract = {Lifetime data analysis or survival analysis is a technique in statistics that can be used to test the durability and reliability of a component. The life time data obtained from the life test experiment is in the form of type I censored data if the life test data is generated after the experiment lasts for a predetermined time. This study aims to obtain a parameter estimator from the exponential distribution of type I censored data using the Linear Exponential Loss Function (LINEX) method. The prior distribution used in this study is a non-informative prior with the technique of determining it using the Jeffrey method. So that the research results were obtained in the form of a parameter estimator θ is  Furthermore, applied to secondary data on the survival time of patients with chronic kidney failure at one of the Bojonegoro Hospitals was carried out in 2014. The data is divided into two, namely data on patients with initial causes of diabetic (data 1) and non-diabetic (data 2) diseases. Based on the estimation results for case studies of patients with chronic kidney failure, the value  = 0.0102608 for patients with initial causes of diabetic disease and  = 0.00712166 for patients with initial causes of non-diabetic disease. This shows that the possibility of patients with initial causes of diabetic disease to fail (die) is higher than patients with non-diabetic causes of disease.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Bayes Estimator Parameters Exponential Distribution of Type I Sensor Data Using Linear Exponential Loss Function Method Based on Prior Jeffrey
AU  - Afriani
AU  - Ardi Kurniawan
AU  - Elly Ana
Y1  - 2023/07/11
PY  - 2023
N1  - https://doi.org/10.11648/j.ijsd.20230902.12
DO  - 10.11648/j.ijsd.20230902.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 62
EP  - 67
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20230902.12
AB  - Lifetime data analysis or survival analysis is a technique in statistics that can be used to test the durability and reliability of a component. The life time data obtained from the life test experiment is in the form of type I censored data if the life test data is generated after the experiment lasts for a predetermined time. This study aims to obtain a parameter estimator from the exponential distribution of type I censored data using the Linear Exponential Loss Function (LINEX) method. The prior distribution used in this study is a non-informative prior with the technique of determining it using the Jeffrey method. So that the research results were obtained in the form of a parameter estimator θ is  Furthermore, applied to secondary data on the survival time of patients with chronic kidney failure at one of the Bojonegoro Hospitals was carried out in 2014. The data is divided into two, namely data on patients with initial causes of diabetic (data 1) and non-diabetic (data 2) diseases. Based on the estimation results for case studies of patients with chronic kidney failure, the value  = 0.0102608 for patients with initial causes of diabetic disease and  = 0.00712166 for patients with initial causes of non-diabetic disease. This shows that the possibility of patients with initial causes of diabetic disease to fail (die) is higher than patients with non-diabetic causes of disease.
VL  - 9
IS  - 2
ER  -

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