Bayesian Estimation of the Mean of a Normal Distribution when the Coefficient of Variation is Known

1983 ◽  
Vol 32 (3) ◽  
pp. 339 ◽  
Author(s):  
S. K. Sinha
Keyword(s):  
Normal Distribution ◽  
Bayesian Estimation ◽  
Coefficient Of Variation ◽  
The Mean

scholarly journals Three-Stage Estimation of the Mean and Variance of the Normal Distribution with Application to an Inverse Coefficient of Variation with Computer Simulation

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 831 ◽  
Author(s):  
Yousef ◽  
Hamdy
Keyword(s):  
Confidence Interval ◽  
Normal Distribution ◽  
Coefficient Of Variation ◽  
Point Estimation ◽  
Squared Error Loss Function ◽  
Sampling Cost ◽  
The Mean ◽  
Interval Problems ◽  
Stage Estimation ◽  
Inverse Coefficient

This paper considers sequentially two main problems. First, we estimate both the mean and the variance of the normal distribution under a unified one decision framework using Hall’s three-stage procedure. We consider a minimum risk point estimation problem for the variance considering a squared-error loss function with linear sampling cost. Then we construct a confidence interval for the mean with a preassigned width and coverage probability. Second, as an application, we develop Fortran codes that tackle both the point estimation and confidence interval problems for the inverse coefficient of variation using a Monte Carlo simulation. The simulation results show negative regret in the estimation of the inverse coefficient of variation, which indicates that the three-stage procedure provides better estimation than the optimal.

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