Bayes Estimator Leads to Classical Estimators under Some Conditions of Prior Distribution for Exponential Distribution: A Simulation Study

by Md. Hasinur Rahaman Khan and Razia Sultana .

Abstract: Maximum likelihood estimation (MLE), uniformly minimum variance unbiased estimation (UMVUE) and minimum mean square error estimation (MMSEE), as classical estimation procedures, are frequently used for parameter estimation in statistics. On the other hand Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding prior distribution. It is of our interest that whether above classical estimators of the parameter for a particular probability distribution can be obtained from Bayes estimator once Bayes estimator is determined. In this analysis one-parameter exponential distribution is used to examine the relationship between Bayesian and classical estimation. Considering improper prior distribution of exponential distribution we have tried to show how the classical estimators can be obtained from Bayes estimator for various choices of the parameters of the prior distribution. Rather than showing this relationship theoretically a simulation has been done to establish that relationship for a particular value of the parameter of exponential distribution. Rossman, Short, and Parks (1998) presented some thought provoking insights on such relationship using continuous uniform and exponential distribution respectively.

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Md. Hasinur Rahaman Khan,
Razia Sultana,

Editor: Dey Sanku,

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