Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

Rizki, Setyo Wira; Mara, Muhlasah Novitasari; Sulistianingsih, Evy

doi:10.1088/1742-6596/855/1/012036

“…There is previous research conducted by Afriani, et al (2023) which discusses parameter estimation of the exponential distribution using the LINEX loss function method with Jeffrey priors on type I censored data. In addition, there is research that proves that the Bayesian LINEX loss function method is able to provide better parameter estimation results than using the Maximum Likelihood Estimator (MLE) method on survival data (Rizki, et al, 2017). Thus, a research update was conducted by estimating parameters using the Bayesian LINEX loss function method for type II censored data on the exponential distribution.…”

Section: Introductionmentioning

confidence: 99%

Bayes Estimator of Exponential Distribution Parameters of Type II Censored Data with Linear Exponential Loss Function Method Based on Jeffrey Priors

Previan,

Kurniawan,

Mardianto

et al. 2023

Jambura J. Probab. Stat.

0

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Survival analysis is often used in the application of analyzing the survival of an object such as living things or objects. This analysis is identical to data censoring which is divided into three, namely: type I, II, and III censored data. Type II censored data is data censoring done by determining the number of objects to be analyzed from the total number of observation objects . Type II censored data is used when the analysis is intended to maximize the results of the analysis. Bayesian Linear Exponential (LINEX) loss function is one method that can be used to estimate parameters in survival analysis by minimizing the expected value of LINEX. The purpose of this study is to determine the Bayesian LINEX loss function parameter estimation on type II censored data using exponential distribution. This method uses the concept of posterior distribution and prior distribution. The prior distribution used is the Jeffrey prior distribution which has objective properties and is based on Fisher information theory The application of the parameter estimation results is carried out on the survival data of lung cancer patients obtained from the North Central Cancer Treatment Group. Based on the results of parameter estimation, it is concluded that the greater the value of the controller (a) can produce a smaller value of parameter estimation results (θ^) . The results of this study can be used as a reference in conducting survival tests using type II censored exponential distribution data using the LINEX loss function method based on Jeffrey priors.

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“…The uniformly minimum risk unbiased (UMRU) estimator under the LINEX loss function can be found using information and facts if there is underestimation and overestimation in real-life situations [ 3 ]. The exponential distribution is a well-known distribution that may be used in a variety of fields, including science, economy, and demographics [ 4 ]. It is a well-known one-parameter distribution that is frequently utilized in model studies [ 5 ].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Mohammed

¹

,

Alaziz

²

,

Sumati

³

et al. 2022

Computational Intelligence and Neuroscience

2

0

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The LINEX loss function, which climbs exponentially with one-half of zero and virtually linearly on either side of zero, is employed to analyze parameter analysis and prediction problems. It can be used to solve both underestimation and overestimation issues. This paper explained the Bayesian estimation of mean, Gamma distribution, and Poisson process. First, an improved estimator for μ 2 is provided (which employs a variation coefficient). Under the LINEX loss function, a better estimator for the square root of the median is also derived, and an enhanced estimation for the average mean in such a negatively exponential function. Second, giving a gamma distribution as a prior and a likelihood function as posterior yields a gamma distribution. The LINEX method can be used to estimate an estimator λ B L ^ using posterior distribution. After obtaining λ B L ^ , the hazard function h B L ^ and D B L ^ the function of survival estimators are used. Third, the challenge of sequentially predicting the intensity variable of a uniform Poisson process with a linear exponentially (LINEX) loss function and a constant cost of production time is investigated using a Bayesian model. The APO rule is offered as an approximation pointwise optimal rule. LINEX is the loss function used. A variety of prior distributions have already been studied, and Bayesian estimation methods have been evaluated against squared error loss function estimation methods. Finally, compare the results of Maximum Likelihood Estimation (MLE) and LINEX estimation to determine which technique is appropriate for such information by identifying the lowest Mean Square Error (MSE). The displaced estimation method under the LINEX loss function was also examined in this research, and an improved estimation was proposed.

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“…

The paper aimed to investigate the performance of some parametric survivor function estimators based on Bayesian methodology with respect to bias and efficiency. A simulation was conducted based on Mote Carlo experiments with different sample sizes different (10, 30, 50, 75, 100). The bias and variance of mean square Error V(MSE) were selected as the basis of comparison.

…”

mentioning

confidence: 99%

Performance of parametric Bayesian Methods for estimating the survivor function in uncensored data using Monte-Carlo simulation

Hassan¹,

Musa²

2021

(GJEB)

0

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The paper aimed to investigate the performance of some parametric survivor function estimators based on Bayesian methodology with respect to bias and efficiency. A simulation was conducted based on Mote Carlo experiments with different sample sizes different (10, 30, 50, 75, 100). The bias and variance of mean square Error V(MSE) were selected as the basis of comparison. The methods of estimation used in this study are Maximum Likelihood, Bayesian with exponential as prior distribution and Bayesian with gamma as prior distribution. A Monte Carlo Simulation study showed that the Bayesian method with gamma as prior distribution was the best performance than the other methods. The study recommended that.

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Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

Cited by 6 publications

References 2 publications

Bayes Estimator of Exponential Distribution Parameters of Type II Censored Data with Linear Exponential Loss Function Method Based on Jeffrey Priors

Bayes Estimator of Exponential Distribution Parameters of Type II Censored Data with Linear Exponential Loss Function Method Based on Jeffrey Priors

Bayesian Estimation of Different Scale Parameters Using a LINEX Loss Function

Performance of parametric Bayesian Methods for estimating the survivor function in uncensored data using Monte-Carlo simulation

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