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

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), 2023. Published by Science Publishing Group

Keywords

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

References
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[2] Harlan, Johan. (2017), Survival Analysisi, Gunadarma Publisher, Depok.
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[4] Fitria, S., Helmi, & Rizki, S. W. (2016), Parameter Estimation of Exponential Distribution of Censored Data Survival Model Using Maximum Likelihood and Bayesian SELF Methods. Math Scientific Bulletin. Stats. and its Application, 3: 213-220.
[5] Sahoo, P. (2008), Probability and Mathematical Statistics. Department of Mathematics University of Louisville, Louisville.
[6] Montgomery, D. C. & Runger, G. C. (2018), Applied Statistics and Probability for Engineers, 7th Edition, John Wiley & Sons, USA.
[7] Guure, C. B., Ibrahim, N. A. & Ahmed, A. O. M. (2012), Bayesian Estimation of TwoParameter Weibull Distribution Using Extension of Jeffrey’s Prior Information with Three Loss Functions, Journal Mathematical Problems in Engineering.
[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.
[14] Al-Noor, Nadia, H., & Bawi, S. F. (2015), Bayes Estimators for the Parameter of the Inverted Exponential Distribution Under Symmetric and Asymmetric Loss Functions Bayes. Journal of Natural Sciences Research, 5 (4), 45–52.
[15] A Wiranto, et al. (2019), Estimation of Type I Cencored Exponential Distribution Parameters Using Objective Bayesian and Bootstrap Methods (Case Study of Chronic Kidney Failure Patients, Journal of Physics: Conference Series.
[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.
Cite This Article
  • 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
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    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
  • Department of Mathematics, Faculty of Science and Technology, Airlangga University, Surabaya, Indonesia

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

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

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