Discuss The Shortest Confidence Interval Based On The Distribution Of Pivot Quantity

The interval estimation of parameter is a basic form for statical conclusion,which can indicate the possible scale for estimated general parameter in a certain extent dependability based on the distribution of pivot quantity.The theory of Neyman confidence interval shows that the certain level of confidence ensures the certain extent dependability,but the precision ofen be scaled by the length of interval.In this article, according to the nonlinear programming theory ,we discusses both the existence and the singleness of the shortest confidence interval, and get the shortest confidence interval with the interrelated method. Compared with the confidence interval with the calculated with traditional method,it has distinct advantage in the paper.Based on the definition of the confidence interval and the numerical calculation method,the minimun confidence interval for exponentially distributed parameters, A comparison of the length of length of the minimum confidence interval with that of the confidence interval calculated with conventional methods shows that in the case of small sample size (n≤11), the adoption of the minimun confidence interval can obviously improve the precision of interval estimation for unkown parameters.