Bayesian Estimator for the Scale Parameter of the Normal Distribution Under Different Prior Distributions
DOI:
https://doi.org/10.33095/jeas.v22i92.466Keywords:
خصائص التوزيع الطبيعي,طريقة الإمكان الأعظم, طريقة العزوم, طريقة بيز , التوزيع الأولي SRIG, التوزيع الأولي non-informative,التوزيع الأولي لعائلة الدالة المرافقة الطبيعية, متوسط مربع الأخطاء (MSE) ,متوسط الخطأ النسبي المطلق (MAPE)., The properties of the normal distribution, Maximum likelihood method, Moment estimation method, Bayes method, the SRIG prior distribution, the non-informative prior distribution, the natural conjugate family of priors, Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE).Abstract
In this study, we used Bayesian method to estimate scale parameter for the normal distribution. By considering three different prior distributions such as the square root inverted gamma (SRIG) distribution and the non-informative prior distribution and the natural conjugate family of priors. The Bayesian estimation based on squared error loss function, and compared it with the classical estimation methods to estimate the scale parameter for the normal distribution, such as the maximum likelihood estimation and the moment estimation. Several cases from normal distribution for data generating, or different sample sizes (small, medium, and large). The results were obtained by using simulation technique, Programs written using MATLAB-R2008a program were used .Simulation results shown that bayes estimation when the prior distribution is (SRIG) distribution with (a=3, b=1) for, and with (a=b=3) for, and with (a=2, b=3) for, and with (a=1, b=3) for gives the smallest value of MSE and MAPE for all sample sizes.
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