استعمال دوال أولية ودالتين خسارة مختلفة لمقارنة مقدرات بيز مع بعض المقدرات الكلاسيكية لمعلمة التوزيع الاسي
DOI:
https://doi.org/10.33095/jeas.v23i99.267الكلمات المفتاحية:
التوزيع الآسي , طريقة الإمكان الأعظم, طريقة العزوم , طريقة بيز , متوسط مربع الأخطاء (MSE) , متوسط مربع الأخطاء الموزونة (MWSE).، The Exponential, Maximum likelihood method, Moment estimation method, Bayes method, mean squared errors (MSE), mean weighted squared errors (MWSE).الملخص
In this study, different estimators were used for estimating parameter of the exponential distribution, such as maximum likelihood estimator, moment estimator and the Bayes estimator, by assuming six types when the prior distribution for the scale parameter is: Levy distribution, Gumbel type-II distribution, Inverse Chi-square distribution, Inverted Gamma distribution, improper distribution, Non-informative distribution .Under squared and weighted squared error loss functions. We used simulation technique, to compare the performance for each estimator, several cases from Exponential distribution for data generating, for different samples sizes (small, medium, and large). Simulation results shown that The best method is the bayes estimation according to the smallest values of MSE & MWSE for all samples sizes (n) comparative to the estimated values by using Maximum likelihood estimation method (MLE) and Moment estimation method (ME). According to obtained results, we see that when the prior distribution for is Inverted Gamma distribution for some values of the parameters , given the best results according to the smallest values of MSE & MWSE comparative to the same values which obtained by using MLE& ME for the assuming true values by and for all samples sizes. When the prior distribution for is Improper distribution for some values of the parameters a & b, given the best results according to the smallest values of MSE & MWSE comparative to the same values which obtained by using MLE & ME for the assuming true values by and all samples sizes.
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