Bayesian estimation of mean and square of mean of normal distribution using linex loss function

1992 ◽  
Vol 21 (12) ◽  
pp. 3369-3391 ◽  
Author(s):  
B.N. Pandey ◽  
Omkar rai
Keyword(s):  
Normal Distribution ◽  
Bayesian Estimation ◽  
Loss Function ◽  
Linex Loss Function ◽  
Linex Loss

scholarly journals E-Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Afrah Al-Bossly
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Shape Parameter ◽  
Likelihood Estimation ◽  
Loss Functions ◽  
Bayesian Estimator ◽  
Linex Loss Function ◽  
Lomax Distribution ◽  
Linex Loss ◽  
Asymmetric Loss Function

The main contribution of this work is the development of a compound LINEX loss function (CLLF) to estimate the shape parameter of the Lomax distribution (LD). The weights are merged into the CLLF to generate a new loss function called the weighted compound LINEX loss function (WCLLF). Then, the WCLLF is used to estimate the LD shape parameter through Bayesian and expected Bayesian (E-Bayesian) estimation. Subsequently, we discuss six different types of loss functions, including square error loss function (SELF), LINEX loss function (LLF), asymmetric loss function (ASLF), entropy loss function (ENLF), CLLF, and WCLLF. In addition, in order to check the performance of the proposed loss function, the Bayesian estimator of WCLLF and the E-Bayesian estimator of WCLLF are used, by performing Monte Carlo simulations. The Bayesian and expected Bayesian by using the proposed loss function is compared with other methods, including maximum likelihood estimation (MLE) and Bayesian and E-Bayesian estimators under different loss functions. The simulation results show that the Bayes estimator according to WCLLF and the E-Bayesian estimator according to WCLLF proposed in this work have the best performance in estimating the shape parameters based on the least mean averaged squared error.

Algorithm for determination of sample size using Linex loss function

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740060
Author(s):  
Wensheng Huang
Keyword(s):  
Analytical Solution ◽  
Sample Size ◽  
Normal Distribution ◽  
Poisson Distribution ◽  
Loss Function ◽  
Linex Loss Function ◽  
Optimal Sample Size ◽  
Optimal Sample ◽  
Linex Loss

The sample size based on the Linex loss function and Blinex loss function is studied in this paper, and the analytical solution of the optimal sample size is deduced on the assumption that the Linex loss function and the normal distribution exist. For the Blinex loss function, an accurate algorithm was presented to obtain the optimal sample size. Furthermore, the optimal sample size is obtained, respectively, by taking Poisson distribution and normal distribution as examples. Due to the wide application of Blinex function in reality, the algorithm presented in this paper has immediate applications.

A Bayesian estimation of reliability model using the linex loss function

1994 ◽  
Vol 34 (9) ◽  
pp. 1519-1523 ◽  
Author(s):  
M. Pandey ◽  
V.P. Singh ◽  
C.P.L. Srivastava
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Reliability Model ◽  
Linex Loss Function ◽  
Linex Loss
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