BAYES ESTIMATION OF EXPONENTIALLY DISTRIBUTED SURVIVAL DATA UNDER SYMMETRIC AND ASYMMETRIC LOSS FUNCTIONS
Abstract
In a research study, population data are often not available, so the population parameter is unknown. Meanwhile, knowledge about the population parameter is needed to know the characteristics of the studied population. Therefore, it is needed to estimate the parameter of the population which can be estimated by sample data. There are several methods of parameter estimation which are generally classified into classical and Bayesian method. This research studied the Bayesian parameter estimation method to determine the parameters of the exponentially distributed survival data associated with the reliability measure of the estimates under symmetric and asymmetric loss functions for complete sample data in a closed form. The symmetric loss functions used in this research are Squared Error Loss Function (SELF) and Minimum Expected Loss Function (MELF). The asymmetric loss functions used are the General Entropy Loss Function (GELF) and Linex Loss Function (LLF). Performance of some loss functions used in this research are then compared through numerical simulation to select the best loss function in determining the parameter estimation of the exponentially distributed survival data. We also studied which loss function is best for underestimation and overestimation modeling. Based on simulation results, the Bayes estimates using MELF is the best method to estimate population parameters of the exponentially distributed survival data for the overestimation modeling, while LLF is the best for the underestimation modeling. We provided direct application in a case study of fluorescence lamp survival data. The results show that the best method to estimate the parameter of the standard fluorescence life data is using LLF for underestimation with and MELF for overestimation with .
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