Abstract: This paper study the way for obtaining confidence limits for parameters by defining an ordering on the sample space, and we focus on statistical models with a real parameter. It is convinced that we should define an ordering on the sample space according to the score function. And it is established that if we define an ordering on the sample space according to the maximum likehood estimate, the resulted confidence limit is the unique root of a strictly increasing function, and we can compute the confidence limit by stochastic approximation.