Abstract: Let X_1, X_2, \cdots, X_n be a sequence of random variables which are independently and identioally distribated on probability spase \left(\Omega, \mathscrF, P_\theta\right)(\theta \in \Theta) with distribution function F(x, \theta). Given t_1, t_2, \cdots, t_n (positive numbers) and g(\theta): \Theta \rightarrow-\infty, \infty. Let Y_i=I\left(X_i>t_i\right) \quad(i=1, \cdots, n), where I(A) is an indicator of the set A.
In the present paper, we give the best lower confidence limits for g(\theta) based on observed Y=\left(Y_1, Y_2, \cdots, Y_n\right). When \Theta=(\underline\theta, \bar\theta)(-\infty \leqslant \underline\theta<\bar\theta \leqslant \infty) and F\left(t_i, \theta\right) is strictly deoreasing for \theta, we obtain an efficient method for constructing the best confidence limit.