تصمیم سازی بهینه در مدل گاما گزینش‌شده تحت یک تابع تعمیم‌یافته

Let $Pi_1,Pi_2$ be two independent gamma populations, where $Pi_i$ has the unknown scale parameter $theta_i$, and the common known shape parameter $alpha>0$. Let $X_{(1)}=min(X_1,X_2)$ and $X_{(2)}=max(X_1,X_2)$. Suppose the population corresponding to the largest $X_{(2)}$ or the smallest $X_{(1)}$ observation is selected. The problem of interest is to estimate the scale parameters $theta_M$ and $theta_J$ of the selected gamma population under a general asymmetric loss function. We characterize admissible and inadmissible estimators of the form $cX_{(2)}$ (or $cX_{(1)}$) within the subclass of invariant estimators of $theta_M$ (or $theta_J$). We derive generalized Bayae estimators of $theta_M$ and $theta_J$ and show that they are linear admissible estimators. Then, we Apply the results for censoring data.