TY - JFULL
AU - Autcha Araveeporn
PY - 2016/10/
TI - An Estimating Parameter of the Mean in Normal Distribution by Maximum Likelihood, Bayes, and Markov Chain Monte Carlo Methods
T2 - International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
SP - 440
EP - 444
EM - kaautcha@hotmail.com
VL - 10
SN - 1307-6892
UR - http://waset.org/publications/10005322
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 117, 2016
N2 - This paper is to compare the parameter estimation of
the mean in normal distribution by Maximum Likelihood (ML),
Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML
estimator is estimated by the average of data, the Bayes method is
considered from the prior distribution to estimate Bayes estimator,
and MCMC estimator is approximated by Gibbs sampling from
posterior distribution. These methods are also to estimate a parameter
then the hypothesis testing is used to check a robustness of the
estimators. Data are simulated from normal distribution with the true
parameter of mean 2, and variance 4, 9, and 16 when the sample
sizes is set as 10, 20, 30, and 50. From the results, it can be seen
that the estimation of MLE, and MCMC are perceivably different
from the true parameter when the sample size is 10 and 20 with
variance 16. Furthermore, the Bayes estimator is estimated from the
prior distribution when mean is 1, and variance is 12 which showed
the significant difference in mean with variance 9 at the sample size
10 and 20.
ER -