Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

International Conference on Mathematics: Education, Theory and Application

数学;教育

Rizki, S.W.^1 ; Mara, M.N.^1 ; Sulistianingsih, E.^1

Mathematics Department of Mathematics and Natural Sciences, Faculty of Tanjungpura University, Indonesia^1

关键词: Bayesian estimations;    Exponential distributions;    Exponential gammas;    Gamma distribution;    Likelihood functions;    LINEX loss function;    Posterior distributions;    Survival Function;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012036/pdf
DOI  :  10.1088/1742-6596/855/1/012036

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior λBLby using Linex approximation. After getting λBL, the estimators of hazard function BLand survival function BLcan be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.