scholarly journals Bayesian Estimation and Prediction of Discrete Gompertz Distribution

2021 ◽  
pp. 1-21
Author(s):  
M. A. Hegazy ◽  
R. E. Abd El-Kader ◽  
A. A. El-Helbawy ◽  
G. R. Al-Dayian
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Hazard Rate ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Gompertz Distribution ◽  
Estimation And Prediction ◽  
Error Loss ◽  
Squared Error ◽  
Rate Functions

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

Bayesian Reliability Estmation with a Truncated Normal Prior

1988 ◽  
Vol 37 (3-4) ◽  
pp. 227-231 ◽  
Author(s):  
Samir K. Bhattacharya ◽  
Ravindar K. Tyagi
Keyword(s):  
Bayesian Estimation ◽  
Parameter Space ◽  
Loss Function ◽  
Exponential Model ◽  
Life Testing ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Squared Error ◽  
Life Tests ◽  
Truncated Normal

Beyesian reliebility estimation for the exponential model. based on life tests that are terminated after a preassigned number of failures, is carried out under the assumption of the squared error loss function and a truncated normal priod density on the parameter space. The Bayesian estimation of reliability for the case of ‘attribute life testing’ is also discussed.

scholarly journals ESTIMASI PARAMETER MODEL SURVIVAL DISTRIBUSI RAYLEIGH PRIOR UNIFORM DENGAN METODE BAYESIAN SELF

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Eka Rizki Wahyuni, Setyo Wira Rizki, Hendra Perdana
Keyword(s):  
Loss Function ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error

Data survival adalah data yang menjelaskan tentang waktu suatu individu atau objek dapat bertahan hingga terjadinya suatu kejadian. Penelitian ini menggunakan metode Bayesian dengan pendekatan Squared Error Loss Function (SELF) untuk melakukan estimasi parameter pada model survival. Proses estimasi parameter metode Bayesian SELF memerlukan informasi dari fungsi likelihood dan distribusi prior yang kemudian akan membentuk distribusi posterior. Hasil dari estimasi parameter metode Bayesian SELF diterapkan pada data kasus penderita kanker paru-paru untuk mengetahui peluang bertahan hidup pasien penderita kanker paru-paru. Kesimpulan dari penelitian ini adalah hasil dari estimasi parameter distribusi Rayleigh prior Uniform dengan menggunakan metode Bayesian SELF menghasilkan nilai survival pada hari ke-95 sebesar 0,929056666 dan nilai hazard 1,549169  sedangkan hari ke-791 menghasilkan nilai survival sebesar 0,006087581 dan nilai hazard sebesar 1,289887 . Hal ini berarti, nilai fungsi survival bergerak mendekati nol sesuai dengan karakteristik fungsi survival dan fungsi hazard yang bergerak naik mendekati satu sesuai dengan karakteristik distribusi Rayleigh. Kata Kunci: Survival, Rayleigh, Bayesian, SELF.

scholarly journals Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

2018 ◽  
Vol 28 (2) ◽  
pp. 162
Author(s):  
Huda A. Rasheed
Keyword(s):  
Loss Function ◽  
Scale Parameter ◽  
Reliability Function ◽  
Rayleigh Distribution ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Mean Squared Errors ◽  
Error Loss ◽  
Squared Error ◽  
Informative Prior

In the current study, we have been derived some Basyian estimators for the parameter and relia-bility function of the inverse Rayleigh distribution under Generalized squared error loss function. In order to get the best understanding of the behavior of Bayesian analysis, we consider non-informative prior for the scale parameter using Jefferys prior Information as well as informative prior density represented by Gamma distribution. Monte-Carlo simulation have been employed to compare the behavior of different estimates for the scale parameter and reliability function of in-verse Rayleigh distribution based on mean squared errors and Integrated mean squared errors, respectively. In the current study, we observed that more occurrence of Bayesian estimate using Generalized squared error loss function using Gamma prior is better than other estimates for all cases

scholarly journals Bayesian Estimation of Parameters of Weibull Distribution Using Linex Error Loss Function

2020 ◽  
Vol 9 (2) ◽  
pp. 38
Author(s):  
Josphat. K. Kinyanjui ◽  
Betty. C. Korir
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Scale Parameter ◽  
Risk Function ◽  
Bayes Estimators ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Error Loss ◽  
Squared Error ◽  
Linex Loss

This paper develops a Bayesian analysis of the scale parameter in the Weibull distribution with a scale parameter  θ  and shape parameter  β (known). For the prior distribution of the parameter involved, inverted Gamma distribution has been examined. Bayes estimates of the scale parameter, θ  , relative to LINEX loss function are obtained. Comparisons in terms of risk functions of those under LINEX loss and squared error loss functions with their respective alternate estimators, viz: Uniformly Minimum Variance Unbiased Estimator (U.M.V.U.E) and Bayes estimators relative to squared error loss function are made. It is found that Bayes estimators relative to squared error loss function dominate the alternative estimators in terms of risk function.

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